An Analysis Of Sertaconazole Nitrate Biology Essay
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Published: Mon, 5 Dec 2016
They are enormous and diverse group of eukaryotic organisms that includes microorganisms such as yeasts and molds. The major difference between fungal cells and plant cells is that the fungal cells have cell walls that contain chitin while the cell walls present in plants contain cellulose. Fungi play an essential and important role in the decay of organic matter and both nutrient cycling and exchange. When fungi overcome the resistance barriers of the human or animal body and establish infections this is called Mycosis  Some fungi has the ability and strength to cause serious diseases in humans such as aspergilloses, cryptococcosis, mycetomas, candidoses, coccidioidomycosis, histoplasmosis, and paracoccidioidomycosis some may be fatal to the infected person if untreated.
. For a long time they have been used as a direct source of food such as mushrooms and truffles also used as a leavening agent for bread, and in fermentation of various food products, such as wine, beer, and soy sauce and Starting at the 1940s the use of fungi for the production of antibiotics. The fungal growth as hyphae on or inside solid substrates or growth as single cells in aquatic environments is adapted for the efficient and quick extraction of nutrients, because those growth forms have high surface area to volume ratios.
Antifungal drugs are classified into two distinctive groups  either drugs used superficial and systemic agents. It should be borne in mind that this differentiation can be arbitrary since some drugs (imidazoles and triazoles, polyenes) may be used in either manner. Various superficial mycoses can be treated either systemically or topically.
Flucytosine (5-fluorocytosine): It’s activated inside the fungal cell by cytosine deaminase to form 5-fluorouracil which undergoes a number of activation steps to form 5-flourodeoxyuridinemonophosphate which inhibits fungal DNA synthesis by binding into RNA causing the inhibition of thymidylate synthesis
Polyene antifungals: The polyene binds with sterols in the fungal cell membrane mainly ergosterol, this changes the transition temperature (TG) of the cell membrane thereby placing the membrane in a less fluid and more crystalline state. As a result the cell’s content leaks and the cell die. Animal cells contain cholesterol instead of ergosterol and so they are much less susceptible to toxicity.
Amphotericin B: a polyene antibiotic related to Nystatin is one of the most effective drugs currently available for the treatment of systemic fungal infections. It is frequently used for the treatment of life-threatening fungal infections in patients with impaired defense mechanisms (e.g., patients which are undergoing immunosuppressive therapy or cancer chemotherapy and patients with AIDS).
Mechanism of Action: The drug is fungistatic and fungicidal as Polyene antifungals.
Other Antifungal Agents
Griseofulvin: Is an antifungal agent and antibiotic produced by Penicillium griseofulvum, it is    active in vitro against most skin disease (dermatophytes) and has been the drug of choice for chronic infections caused by these fungi since it is orally administered and apparently integrated into actively growing tissue. Till now they are still used in such instances but is being competed by some of the newly discovered azole antifungal agents it inhibits mitosis in fungi. Two other classes for treatment of topical dermatomycoses they are of recently discovered antifungal classes represent a new addition, the two allylamines (naftifine and terbinafine) inhibit ergosterol synthesis (as imidazoles) at the level of squalene epoxidase; one morpholene derivative (amorolfine) inhibits at a subsequent step in the ergosterol pathway.
Benzoic acid – has antifungal properties but should be combined with a keratolytic agent.
Imidazoles and Triazoles
They are synthetic antifungal drugs that inhibit the enzyme cytochrome P450 which is necessary in fungal cell membrane synthesis; they have the same antifungal spectrum and mechanism of action. The systemic triazoles have slower metabolized and have less effect on human sterol synthesis than do the imidazoles.
Miconazole – miconazole nitrate
Clotrimazole – marketed Econazole
Sertaconazole – marketed as Ertaczo in North America
Selection of Antifungal Agents
Susceptibility testing with the fungi in vitro is not commonly used as drugs active in vitro do not always work or give the same results in vivo, so tests to determine the use of a certain antifungal drug based of the specific fungal pathogen involved. Antifungals spectrum is predetermined through preclinical and clinical testing with the most common fungal pathogens and the results of preclinical and clinical testing would determine the spectrum, this help to select the suitable antifungal agent for each fungal infection. Resistance to antifungal agents has become increasing problem.
The recent fungal resistance to the azole antifungal drugs is considerably complicated and now is under evaluation. Examples of both primary and secondary fungal resistance are known for the medically important yeasts and the selected azole antifungal drugs. Example of antifungals resistance Candida krusei as a species is usually resistant to fluconazole and Candida albicans strains are usually susceptible to fluconazole and certain other azole antifungal drugs, but there are increasing reports of resistance, especially in HIV positive infected hosts having undergone previous repeated courses of azole antifungal therapy. The question of drug resistance is complicated due to the limitations found in the available susceptibility testing methods and the ability to differentiate between microbiological and clinical drug resistance. When an inhibitory antifungal agent reaches the peak of its activity in a host with a lowering or decreasingly efficient immune system occurs at latter.
Systematic (IUPAC) name
Sertaconazole is a member of imidazole antifungal group used topically as the nitrate as a 2% in the form of cream, gel, solution, or powder as it have negligable bioavalibility its used in the treatment of superficial candidiasis, dermatophytosis, seborrhoeic dermatitis, , pityriasis versicolor. A single dose of Sertaconazoles antimicrobial activity equals or surpasses that of miconazole, tioconazole or bifonazole. It has been recommended for the treatment of cutaneous dermatoses, vaginal candidiasis, usually used two times daily for 4 weeks.
Sertaconazole nitrate is a white or almost white powder. It is practically insoluble in water, sol-uble in methanol, sparingly soluble in alcohol and in methylene chloride. Each gram of Dermofix ® Cream, 2%, contains 17.5 mg of sertaconazole (as sertaconazole nitrate, 20 mg) in a white cream base of ethylene glycol and polyethylene glycol palmitostearate, glyceryl isostearate, light mineral oil, methylparaben, polyoxyethylened saturated glycerides and glycol-ized saturated glycerides, sorbic acid and purified water.
Mechanism of action
Sertaconazole posses different mechanisms as it’s fungicidal & fungistatic also it can be used as antibacterial, antipyretic and anti-inflammatory activity. As other imidazole antifungals it inhibits the synthesis of ergosterol by inhibiting the 14Î±-demethylase enzyme. This inhibits the synthesis of fungal cell membrane which prevents the fungus from growing & multiplying, this is its fungistatic activity.
For the fungicidal action of sertaconazole it contain benzothiophene ring in its structure which is similar to tryptophan found on the fungal membrane so the benzothiophene ring takes its place on the fungal membrane leading to the formation of pores that open after a short period of time (about 10 minutes) causing leakage of intracellular content mainly ATP so fungus lacks energy and die. Sertaconazole is the only antifungal which possesses this unique mechanism of action.
Sertaconazole is a topical antifungal that is a member of the imidazole class of antifungals. While the mechanism of action of the imidazole antifungals is not yet known, it is believed that they act primarily by inhibiting the inhibiting the 14Î±-demethylase enzyme which inhibit the synthesis of ergosterol. Ergosterol is an important component of the cell membrane of fungi the lack of this component leads cell injury mainly by leakage of cellular constituents in the cytoplasm from the cell.
Dry skin may occur
If any of these symptoms persist or get worse stop the use of the drug and consult the physician many people using this medication do not experience any serious side effects. A severe allergic reaction to this drug is unlikely, but seeks instant medical attention if it occurs.
Some of the symptoms of a serious allergic reaction include:
Trouble in breathing
A white or almost white powder, practically insoluble in water, soluble in methanol, sparingly soluble in alcohol, in methylene chloride.
Pharmacopoeias. In Euro.
Ph. Euro. 6.2 (Sertaconazole Nitrate). A white or almost white powder. Virtually insoluble in water; sparingly soluble in alcohol, in dichloromethane; soluble in methyl alcohol. Protect from light.
A. Melting point: 156 °C to 161 °C.
B. Ultraviolet and visible absorption spectrophotometry
Test solution Dissolve 0.1 g in methanol R and dilute to 100 ml with the same solvent. Dilute 10 ml of this solution to 100 ml with methanol R. Spectral rangeÄ±240-320 nm.
Absorption maxima at 260 nm, 293 nm and 302 nm.
Absorbance ratioÄ±A302/A293 = 1.16 to 1.28.
C. Infrared absorption spectrophotometry
Preparation Dry the substances at 100-105 °C for 2 h and examine as discs of potassium bromide R.
Comparison sertaconazole nitrate CRS.
D. Thin-layer chromatograph
Solvent mixture concentrated ammonia R, methanol R (10:90 V/V).
Test solution Dissolve 40 mg of the tested substance to be examined in the solvent mixture and dilute to 10 ml with the solvent mixture.
Reference solutions (a) Dissolve 40 mg of sertaconazole nitrate CRS in the solvent mixture and dilute to 10 ml with the solvent mixture.
Reference solution (b) Dissolve 20 mg of miconazole nitrate CRS in reference solution (a) and dilute to 5 ml with reference solution (a).
Plate TLC silica gel G plate R.
Mobile phase concentrated ammonia R, toluene R, and dioxan R (1:40:60 V/V/V).
Development over a path of 15 cm.
Drying in a current of air for 15 min.
Detection expose to iodine vapour for 30 min.
System suitability reference solution (b): the chromatogram shows 2 clearly separated spots.
The results in the principal spot in the chromatogram obtained with the test solution are similar in position, colour and size to the principal spot in the chromatogram obtained with reference solution (a).
E. about 1 mg gives the reaction of nitrates.
Appearance of solution
The solution is clear and not more intensely colored than reference solution Y5. 
Dissolve 0.1 g in ethanol (96 per cent) R and dilute to 10 ml with the same solvent.
Test solution: Dissolve 10.0 mg of the substance to be examined in the mobile phase and dilute to 10.0 ml with the mobile phase.
Reference solution (a): Dilute 5.0 ml of the test solution to 100.0 ml with the mobile phase. Dilute 1.0 ml of this solution to 20.0 ml with the mobile phase.
Reference solution (b): Dissolve 5.0 mg of sertaconazole nitrate CRS and 5.0 mg of miconazole nitrate CRS in the mobile phase and dilute to 20.0 ml with the mobile phase. Dilute 1.0 ml of this solution to 50.0 ml with the mobile phase.
Size: l = 0.25 m, Ø = 4.0 mm;
Stationary phase: nitrile silica gel for chromatography R1 (10 Î¼m).
Mobile phase acetonitrile R1, 1.5 g/l solution of sodium dihydrogen phosphate R (37:63 V/V).
Flow rate 1.6 ml/min.
Detection Spectrophotometer at 220 nm.
Injection 20 Î¼l.
Run timeÄ±1.3 times the retention time of sertaconazole.
Retention time Nitrate ion = about 1 min; miconazole = about 17 min; sertaconazole = about 19 min.
System suitability Reference solution (b):
Resolution: minimum 2.0 between the peaks due to miconazole and sertaconazole.
Limits: Impurities A, B, C: for each impurity, should not exceed the area of the principal peak in the
Chromatogram obtained with reference solution (a) (0.25 per cent);total: not more than twice the area of the principal peak present in the chromatogram obtained with reference solution (a) (0.5 per cent);
Disregard limit: 0.2 times the area of the principal peak in the chromatogram obtained with reference solution (a) (0.05 per cent); disregard the peak due to the nitrate ion.
Maximum 1.0 per cent, determined on 0.50 g.
Maximum 0.1 per cent, determined on 1.0 g.
Dissolve 0.400 g in 50 ml of a mixture of equal volumes of anhydrous acetic acid R and methyl ethyl ketone R. Titrate with 0.1 M perchloric acid, determining the end-point potentiometrically. Carry out a blank titration.
1 ml of 0.1 M perchloric acid is equivalent to 50.08 mg of C20H16Cl3N3O4S.
STORAGE: Protected from light.
Specified impurities A, B, C.
Methods of Analysis
– Infrared absorption spectrophotometer.
– Ultraviolet and visible absorption spectrophotometer.
– Mass spectrometry.
– Thin-layer chromatograph (TLC).
– High performance liquid chromatography (HPLC).
1- Authentic Sample
Pure samples of Sertaconazole nitrate, was kindly supplied by October pharma Pharmaceutical Co. – Egypt. The purity of the samples was found to be 100.29 + 0.302%, 100.12 + 0.437%, 100.22 + 0.388% and 100.25 + 0.511% according to the reported HPLC method.
2- Market Samples
® (powder, cream & solution)
Dermofix ® cream, Batch No. 5AE0005, labeled to contain 15 mg of Sertaconazole nitrate per each one gram of cream and Dermofix ® cream, Batch No. 021111, each one gram is claimed to contain 10 mg of Sertaconazole nitrate. Creams are manufactured by October pharma Pharmaceutical Co. – Egypt under Licence of ORTHO PHARMACEUTICAL CORP.
3-Chemicals and Solvents:
Methanol ( E. Merck, Darmstadt – FRG)
Acetonitrile (HPLC grade, E. Merck, Darmstadt – FRG)
Formic acid ( E. Merck, Darmstadt – FRG)
All organic solvents used were of spectroscopic grade
A. UV-visible spectrophotometer
UV-visible spectrophotometer, UV-Probe 1800 version 2.32 (Shimadzu, Kyoto – Japan) with matched 1-cm quartz cells, connected to an IBM compatible personal computer (PC) and a HP-600 inkjet printer.
High performance liquid chromatograph composed of a quaternary pump (1200 series, G 1311A) with an ultraviolet variable wavelength detector, 1200 series (Agilent Technologies, Waldbronn, – Germany) and a equipped with 20-l injector loop. Manual injector model 7725 I (USA). Dual-beam UV-visible spectrophotometer, UV-Probe 1800 version 2.32 (Shimadzu, Kyoto – Japan) with matched 1-cm quartz cells, connected to an IBM compatible personal computer (PC) and a HP-600 inkjet printer.
A. Standard Solution for the Intact Drug
0.05 gm of intact sertaconazole samples was accurately weighted and transferred into a 50 ml measuring flask and volume was completed with methanol.
B. Standard Solution for the Degrdate
0.05 g of pure Sertaconazole were accurately weighed and transferred to a 100-ml round bottomed flask and 20 ml of conc. HCl were added. Reflux for 5 hours was done. The solution was concentrated to near dryness under vacuum, cooled to room temperature (25 0C), then quantitatively transferred with methanol to a 100-ml measuring flask, completed to volume with the same solvent. 2 ml of each solution (intact drug and the degredate) was transferred separately into a 25- ml measuring flask then volume is completed with methanol. Various concentrations was then made and measured at 200-400 nm.
Complete degradation is confirmed by HPLC method
A ZORBAX-ODS Column (250 x 4.6 mm, i.d.), particle size (5 mm), (Agilent Technologies, Waldbronn-Germany),
Methanol: 0.2% formic acid aqueous solution (70:30, v/v,) at the flow rate of 1.0 mL/min.
Detection: the eluted analytes were detected at 260 nm.
Suggested Degradation pathway of Sertaconazole
/ 5 hrs, reflux
N-(2-(2,4 dichlorophenyl)-2-hydroxy) ethylimidazole.
C. Standard Solution for the Cream
1 gm of the cream was accurately weighted and placed in a beaker, 20 ml ethanol was added and the beaker placed on the water bath till the cream totally dissolved then the beaker was placed in the refrigerator for 15 minutes then filtered. The sample in the beaker was the filtered and the process was repeated for 4 times to insure that the amount of drug (sertaconazole) completely dissolved in the methanol then the volume was completed in a conical flask to 50 ml and various concentrations were made and measured in spectrophotometer at 200-400 nm
D. Standard Solution for the powder
1 gm of the powder was accurately weighted and placed in a beaker, 20 ml ethanol was added and the beaker placed on magnetic stirrer for 15 min till the powder completely dissolved in the methanol then the volume was completed in a conical flask to 50 ml and various concentrations were made and measured in spectrophotometer at 200-400 nm.
Definition: The first (second, …) derivative absorption spectrum of a molecule is defined as the first (second, …) derivative, dA(n ~ ) ¤ dn ~ , [dA(n ~ ) ¤ dn ~2, ¼] of the absorbance A as a function of wave number, n ~ . Wavelengths may be used in place of wave numbers but the shape of the derivative spectra will be slightly different. When derivative spectra are obtained at low temperature, they are called first (second …) derivative low temperature absorption spectra (specifying the solvent, temperature and solute concentration). In spectroscopy, the differentiation of spectra is a widely used technique, particularly in infra-red, UV.-visible absorption, fluorescence, and reflectance spectrophotometry, referred to as derivative spectroscopy. Derivative methods have been used in analytical spectroscopy for three main purposes: (a) spectral discrimination, as a qualitative fingerprinting technique to accentuate small structural differences between nearly identical spectra; (b) spectral resolution enhancement, as a technique for increasing the apparent resolution of overlapping spectral bands in order to more easily determine the number of bands and their wavelengths; (c) quantitative analysis, as a technique for the correction for irrelevant background absorption and as a way to facilitate multi-component analysis. (Because differentiation is a linear technique, the amplitude of a derivative is proportional to the amplitude of the original signal, which allows quantitative analysis applications employing any of the standard calibration techniques). Most commercial spectrophotometers now have built-in derivative capability. Some instruments are designed to measure the spectral derivatives optically, by means of dual wavelength or wavelength modulation designs. Because of the fact that the amplitude of the nth derivative of a peak-shaped signal is inversely proportional to the nth power of the width of the peak, differentiation may be employed as a general way to discriminate against broad spectral features in favor of narrow components. This is the basis for the application of differentiation as a method of correction for background signals in quantitative spectrophotometric analysis. Very often in the practical applications of spectrophotometry to the analysis of complex samples, the spectral bands of the analyte (i.e. the compound to be measured) are superimposed on a broad, gradually curved background. Background of this type can be reduced by differentiation.
This is illustrated by the figure on the left, which shows a simulated UV spectrum (absorbance vs wavelength in nm), with the green curve representing the spectrum of the pure analyte and the red line representing the spectrum of a mixture containing the analyte plus other compounds that give rise to the large sloping background absorption. The first derivatives of these two signals are shown in the center; you can see that the difference between the pure analyte spectrum (green) and the mixture spectrum (red) is reduced. This effect is considerably enhanced in the second derivative, shown on the right. In this case the spectra of the pure analyte and of the mixture are almost identical. In order for this technique to work, it is necessary that the background absorption be broader (that is, have lower curvature) than the analyte spectral peak, but this turns out to be a rather common situation. Because of their greater discrimination against broad background, second (and sometimes even higher-order) derivatives are often used for such purposes. It is sometimes (mistakenly) said that differentiation “increases the sensitivity” of analysis. You can see how it would be tempting to say something like that by inspecting the three figures above; it does seems that the signal amplitude of the derivatives is greater (at least graphically) than that of the original analyte signal. However, it is not valid to compare the amplitudes of signals and their derivatives because they have different units. The units of the original spectrum are absorbance; the units of the first derivative are absorbance per nm, and the the units of the second derivative are absorbance per nm2. You can’t compare absorbance to absorbance per nm any more than you can compare miles to miles per hour. (It’s meaningless, for instance, to say that 30 miles per hour is greater than 20 miles.) You can, however, compare the signal-to-background ratio and the signal-to-noise ratio. For example, in the above example, it would be valid to say that the signal-to-background ratio is increased in the derivatives.
A spectrum that is the result of applying a derivative transform to the data of the original spectrum. Derivatives of spectra are very useful for two reasons:
1. First and second derivatives may swing with greater amplitude than the primary spectra. For example, a spectrum suddenly changes from a positive slope to a negative slope, such as at the peak of a narrow feature (see the figure below). The more distinguishable derivatives are especially useful for separating out peaks of overlapping bands.
2. In some cases derivative spectra can be a good noise filter since changes in base line have negligible effect on derivatives. For example, scattering increases with wavelength for some biologically active macromolecules causing an increasing slope of the absorbance baseline. A commonly used approximation of the first derivative is:
dÎ±/dÎ» = [Î± (Î» + Î”Î») – Î± (Î» – Î”Î»)] / 2Î”Î».
A more accurate approximation of the first and higher order derivatives is presented in thorough explanations by Whitaker1 and Morrey2. Still other methods involve a best fit match to the curve on the features of interest and performing higher order derivatives with numerical analysis.
Derivative spectra yield good signal-to-noise ratios only if the difference of noise levels at the endpoints of the interval is small enough to yield a noise equivalent Î”dÎ±/dÎ» calculation much smaller than the absorbance.
Uses of Derivative Spectroscopy
Derivative spectroscopy uses first or higher derivatives of absorbance with respect to wavelength for qualitative analysis and for quantification. The concept of derivatizing spectral data was first introduced in the 1950s, when it was shown to have many advantages. However, the technique received little attention primarily because of the complexity of generating derivative spectra using early UV-Visible spectrophotometers. The introduction of microcomputers in the late 1970s made it generally practicable to use mathematical methods to generate derivative spectra quickly, easily and reproducibly. This significantly increased the use of the derivative technique. In this application note we review briefly the mathematics and generation methods of derivative spectroscopy. We illustrate the features and applications using computer-generated examples.
If a spectrum is expressed as absorbance, A, as a function of wavelength, the , derivative spectra are:
Figure shows a computer simulation of the effects of derivatization on the appearance of a simple Gaussian absorbance band. Derivative spectra are always more complex than zero order spectra. A first-order derivative is the rate of change of absorbance with respect to wavelength. A first order derivative starts and finishes at zero. It also passes through zero at the same wavelength as of the absorbance band. Either side of this point is positive and negative bands with maximum and minimum at the same wavelengths as the inflection points in the absorbance band. This bipolar function is characteristic of all odd-order derivatives. The most characteristic feature of a second-order derivative is a negative band with minimum at the same wavelength as the maximum on the zero-order band. It also shows two additional positive satellite bands either side of the main band. A fourth-order derivative shows a positive band. A strong negative or positive band with minimum or maximum at the same wavelength as of the absorbance band is characteristic of the even-order derivatives. Note that the number of bands observed is equal to the derivative order plus one.
If we assume that the zero-order spectrum obeys Beer’s law, there is a similar linear relationship between concentration and amplitude for all orders of derivative
For single component quantification the selection of wavelengths for derivative spectra is not as simple as for absorbance spectra because there are both positive and negative peaks. For the even order derivatives there is a peak maximum or minimum at the same as the absorbance spectrum but for the odd-order derivatives this wavelength is a zero crossing point. Taking the difference between the highest maximum and the lowest minimum gives the best signal-to noise ratio but may lead to increased sensitivity to interference from other components.
Obtaining derivative spectra
Derivative spectra can be obtained by optical, electronic, or mathematical methods. Optical and electronic techniques were used on early UV-Visible spectrophotometers but have largely been superseded by mathematical techniques. The advantages of the mathematical techniques are that derivative spectra may be easily calculated and recalculated with different parameters, and smoothing techniques may be used to improve the signal-to-noise ratio.
Optical and electronic techniques
The main optical technique is wavelength modulation, where the wavelength of incident light is rapidly modulated over a narrow wavelength range by an electromechanical device. The first and second derivatives may be generated using this technique. It is popular for dedicated spectrophotometer designs used in, for example, environmental monitoring. First-derivative spectra may also be generated by a dual wavelength spectrophotometer. The derivative spectrum is generated by scanning with each monochromator separated by a small constant wavelength difference. First and higher-order derivatives can be generated using analog resistance capacitance devices. These generate the derivative as a function of time as the spectrum is scanned at constant speed (dA/dt=S). For the first derivative:
Higher-order derivatives are obtained by using successive derivators. The electronic method suffers from the disadvantage that the amplitude and wavelength shift of the derivatives varies with scan speed, slit width, and resistance- capacitance gain factor.
To use mathematical techniques the spectrum is first digitized with a sampling interval of. The size of depends on the natural bandwidth (NBW) of the bands being processed and of the bandwidth of the instrument used to generate the data. Typically, for UV-Visible spectra, the NBW is in the range 10 to 50 nm. Firstderivative spectra may be calculated simply by taking the difference in absorbance between two closely spaced wavelengths for allwavelengths :
Where the derivative amplitude, , is calculated for a wavelength intermediate between the two absorbance wavelengths. For the second-derivative determination three closely-spaced wavelength values are used:
Higher-order derivatives can be calculated from similar expressions. This method involves simple linear interpolation between adjacent wavelengths. A better method is that proposed by Savitzky and Golay. To calculate the derivative at a particular wavelength, , awindow of ±n data points is selected and a polynomial is fitted using the least squares method:
An advantage of this method is that it can be used to smooth the data. If the polynomial order, l, is less than the number of data points (2n+1) in the window, the polynomial generally cannot go through all data points and thus the least squares fit gives a smoothed approximation to the original data points. This feature can be used to counteract the degradation of signal-to-noise that is inherent in the derivatization process (see below). The coefficients a0…al at each wavelength multiplied by the factorial of the order are the derivative values: a1 is the first derivative, 2xa2 the second derivative, 6xa3 the third derivative, and so on.
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