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.