Special Polynomials v0.1 (beta)
		===============================

Warning:	This library is beta version.
		P.nm and Y.nm handling for negative m is suspect.
		<Name>.nm handling for |m| > n is suspect.

This library needs ALG48 v2.1 to work. Also, due to the special speedup
tricks used in ALG48, in GX this library must be stored either in the same
port as ALG48 or in port 0.

Package contents:

	spoly.doc	This documentation
	spoly.bz	BZipped source code directory (Jazz)
	spoly.lib	The binary

The library provides commands for generating:


	P	Legendre polynomials
	 n

	 m
	P	Associated Legendre functions
	 n

	 m
	Y	Spherical harmonics
	 n

	H	Hermite functions
	 n

	T	Tschebyscheff polynomials
	 n

	U	Tschebyscheff polynomials (Type II)
	 n

	L	Laguerre polynomials
	 n

	 m
	L	Associated Laguerre polynomials
	 n

In addition the library provides a command for calculating factorial for
a positive integer argument with infinite precision. The command ZS is a
faster version of the Z<->S command in ALG48, and will probably be integrated
into it later.

Stack syntax:

	P.n	( %n x --> sym )
	P.nm	( %n %m x --> sym )
	Y.nm	( %n %m phi alpha --> sym )
	H.n	( %n x --> sym )
	T.n	( %n x --> sym )
	U.n	( %n x --> sym )
	L.n	( %n x --> sym )
	L.nm	( %n %m x --> sym )
	FACTOR	( %n --> %f | $ )
	ZS	( Z --> $ )
		( $ --> Z )
		( % --> Z )

The dotted names were chosen so that the names would be displayed nicely
with the EQSTK library (v4.2 or higher).

Examples:

14 FACTOR	= 87178291200
15 FACTOR	= "1307674368000"		; too many decimal digits for %
1.2 FACTOR	= 1.10180249088			; regular built-in factorial


		  1    5    3
5 X P.n		= -(63X -70X +15X)		; Standard output form
		  8

		           2 1/2
2 1 X P.nm	= 3*X*(1-X )			; Regular output


2 1 COS(x) P.nm	= 3*COS(X)*SIN(X)		; Special output for COS

		      _____
		     |  5                 ip
2 1 t p Y.nm	= -  |-----*3COS(t)SIN(t)e	; Usually t,p = theta, phi
		    \|24*PI


Actual order of terms may vary with ALG48 version, especially in ALG48 v2.1
integers tend to come out after variable terms (to be fixed).