The Users\SpecialFunctions subdirectory of Derive includes special function packages contributed free of charge by Derive users.  If you have any questions about a package, please contact the author of the package directly.

CarlsonEllipticIntegrals.mth   Defines efficient, high precision functions for numerically approximating the Carlson elliptic integrals RF(x,y,z), RJ(x,y,z,p), RC(x,y), RD(x,y,z), and RG(x,y,z), and the Legendre elliptic integrals ELLIPTIC_F(phi,m), ELLIPTIC_E(phi,m), and ELLIPTIC_PI(phi,m,n) with real or complex arguments.  The algorithms are based on Numerical Algorithms 10(1995)13-26, B.C. Carlson, Numerical computation of real or complex elliptic integrals.

EulerMaclaurinSummation.mth   Defines functions for approximating finite or infinite sums using an asymptotic expansions based on the Euler-Maclaurin series approximation formula.  The formula is described on page 806, Section 23.1.30 of the Handbook of Mathematical Functions by Milton Abramowitz and Irene A. Stegun.

ProbabilityDistributions.dfw   Defines functions for approximating cumulative F, t, and Chi-square distributions and their inverses, even for problems having large degrees of freedom.  Since these distribution functions are defined in terms of the incomplete beta and incomplete gamma functions, routines for approximating these functions and their inverses are also included in the package.

SpecialFunctions.dfw and SpecialFunctions.mth   Defines functions for computing special functions and their derivatives.  Functions include exponential integrals, incomplete gamma function, polygamma function, incomplete beta function, error integrals, orthogonal polynomials, elliptic integrals, Weierstrass elliptic functions, Bessel functions, Airy functions, confluent hypergeometric functions, Coulomb wave functions, and Gauss’ hypergeometric functions.


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