This section contains specialized mathematical functions used in ATMTools.
Name |
Description |
Computes the value of the Fresnel sine and cosine integrals $C(x) - i S(x) = int_0^x dt e^{-ipi t^2/2}$. Will either approximate or use quadl to compute, depending on the flag est. est = TRUE (default) for approximation, FALSE for quadl integration. Note that both $C(x)$ and $S(x)$ have odd symmetry, therefore, one need only compute for positive values of x. | |
Returns the complex hypergeometric $_aF_b({A};{B};{x})$ function using a series approximation with N terms where a is the length of the vector A and b is the length of the vector B. | |
Asymptotic approximation of $_2F_3({B},{D},-{z})$, z >> 1. This routine calculates the asymptotic expression for the generalized hypergeometric funcion for the case for which there are two numerator parameters and three denominator parameters. The asymptotic expression approximates $_2F_3({B},{D},-{z})$ when Z is large and positive. | |
Computes values of the Lommel functions L and M using U and V Lommel functions to within an absolute tolerance of tol. If tol is an integer, TOL terms will be used in the series expansion. | |
Function to calculate the ratio of gamma functions as defined in Sasiella's book. $Gamma(a,b) = Gamma(a1)*Gamma(a2)*...*Gamma(ap)/ (Gamma(b1)*Gamma(b2)*...*Gamma(bq))$ where a and b are vectors of length p and q respectively. | |
Computes the radial and azimuthal order of Zernike polynomial using Noll's ordering scheme. |
Copyright (c) 2009. All rights reserved.
|
What do you think about this topic? Send feedback!
|