CSpecFn BETA 0.11 Special Functions (C implementation) Author: Bhuvanesh Bhatt (bbhatt1@towson.edu) Platforms: TI-89 and TI-92 Plus Last updated: August 12, 2001 C functions in this package: * BesselJ(n,x) returns the Bessel J function of order n Requirements: x>=0, n>=0, n<50. Both x and n must be real. Examples: BesselJ() shows a help message in the status line BesselJ(1.3,2.7) returns the Bessel J function for orders upto the given n * ExpIntE(n,x) returns the Exponential integral E for order n Requirements: x must be positive, and n must be nonnegative. Both x and n must be real. Examples: ExpIntE() shows a help message in the status line ExpIntE(21,1.12) returns 0.015408474674 Note: This is Integral(e^(-z*t)/t^n,t,1,infinity), but nInt() fails. * ExpIntEi(x) returns the Exponential integral Ei Requirement: x must be real and nonzero. Examples: ExpIntEi() shows a help message in the status line ExpIntEi(3.724) returns 16.2252926976 Note: This is -Integral(e^(-t)/t,t,-z,infinity) for z>0, but nInt() fails. * Fresnel(x) returns {FresnelC(x),FresnelS(x)} Requirement: x must be real. Examples: Fresnel() shows a help message in the status line Fresnel(4.1) returns {.573695631451,.475798257033} Note: This is an alternative to using nInt() to compute the integrals. * Gamma(a[,x[,epsilon]]) returns the incomplete gamma function Examples: Gamma() shows a help message in the status line Gamma(5) returns the "regular" gamma function Gamma(-1,2) returns the incomplete gamma function Gamma(1.1,100,1*10^-6) returns the incomplete gamma function with accuracy 1*10^-6 Note: The default accuracy is "full accuracy" (1*10^-14) * Psi(x) returns the Digamma function Requirement: x must be real. Examples: Psi() shows a help message in the status line Psi(1) returns .577215664902 Psi(-1.000001) returns 1000000.42278 Psi(10^500) returns 1151.2925465 * Zeta(x[,a[,epsilon]]) returns the Hurwitz zeta function Requirements: x and a must be real, and x>1. Also, do not try integers for x, because incorrect values are returned. Examples: Zeta() shows a help message in the status line Zeta(1.1) returns the Riemann zeta function Zeta(1.1,1.1) returns the Hurwitz zeta function Zeta(4.2,5.0,1*10^-6) returns the Hurwitz zeta function with accuracy 1*10^-6 Note: The default accuracy is "full accuracy" (1*10^-14) Future plans: * Improve accuracy of Zeta for integer values of x * Perhaps integrate all these special functions into a Flash app Disclaimer: This is a beta version and has not been tested for either stability or accuracy. It may crash or hang. I am not responsible for any damage done to your calculator. To reset the calculator, press: [2nd][LOCK][ON] on the TI-92 Plus [2nd][LEFT][RIGHT][ON] on the TI-89 If this doesn't reset the calculator, take out a battery, press and hold [(-)][)] while you insert the battery. Of course, this does not mean your calculator will definitely crash or hang :) In fact, you should be able to break a calculation by pressing [ON]. Copyright Bhuvanesh Bhatt.