SPFNS1 - A Special Function File for the HP-41 written by Sherman
Lowell, CHHU 26,HPX 27,HPCC 522,PPC-Paris 396, NE 1610 Upper Dr,
Pullman, WA 99163, Tel 509-332-7512.

The SPFNS1 HP-41 file contains several useful mathematical
functions: the Gamma Function of x, which is a generalization to
arbitrary real numbers of the built-in factorial function (x-1)!,
the Psi Function of x, which is the derivative of Gamma(x), the
Incomplete Gamma Function of parameter a and of x, the
Exponential Integral Function of x, which is the special case a=0
of the Incomplete Gamma Function, the Exponential Integral
Function of x of order n, which equals the Incomplete Gamma
Function multiplied by x^(-a) with a=1-n, and, finally the Chi
Square Probability Function of "chisquare" and n, also related to
the Incomplete Gamma Function. More information about these and
the functions defined in files SPFNS2 and ELFNCS can be found in
the books: 1) J. Spanier and K. B. Oldham, "An Atlas of
Functions," Harper & Row, New York, 1987; 2) M. Abramowitz and L.
A. Stegun (eds.), "Handbook of Mathematical Functions," U. S.
Government Printing Office, 1964 (also available as a reprint
from Dover Publications, New York).

All the functions in SPFNS1 work in any HP-41 without special
modules. LBL"GAMX" and LBL"PSIX" do not use any numbered storage
registers; LBL"IGAMXA", LBL"EINTX", LBL"EINTXN", and LBL"CSQXN"
require SIZE 020. Variables are entered in the order in which
they appear in the labels, e.g., GAMX expects x in the X-register
and IGAMXA expects x in Y- and a in X-register. The result is
returned in X-register and the value of x is in LASTX, like the
built-in functions, though other stack registers are altered. The
computational algorithms have been optimized for a combination of
speed and accuracy. The maximum error of all functions is
believed to be < 5.E-8. If the function value is + or - infinity,
the algorithm returns 1.E99 without causing an overflow error.
The advantage of this is that, when used as a subroutine,
the large value in a denominator will allow the main routine to
continue with negligible error.

The algorithms used in SPFNS1 will be described in an article to
appear in HPX or HPCC. If you encounter any problems with the
routines, I would appreciate your reporting them to me. X<>Y