Toronto Function for the HP-41

Overview
 

Toronto function is defined by

   T(m,n,r) = exp(-r²) [ Gam((m+1)/2) / n! ] r^2n-m+1  M( (m+1)/2 , n+1 , r² )

where M(a,b,x) = Kummer's function
 

Program Listing
 

Data Registers:   R00 thru R04: temp
Flags: /
Subroutines:   "KUM"  ( cf "Kummer's Function for the HP-41" )
                          "GAM" or "GAM+" ...  ( cf "Gamma Function for the HP-41" )
 
 

01  LBL "TOR"  02  STO 03 03  CLX 04  SIGN 05  + 06  STO 02 07  X<>Y 08  STO 04

09  LASTX 10  + 11  2 12  / 13  STO 01 14  RCL 03 15  X^2 16  XEQ "KUM"

17  RCL 00 18  CHS 19  E^X 20  * 21  X<> 01 22  XEQ "GAM" 23  ST* 01 24  RCL 02

25  XEQ "GAM" 26  ST/ 01 27  RCL 01 28  RCL 03 29  RCL 02 30  ST+ X 31  1 32  -

33  RCL 04        34  - 35  Y^X 36  * 37  END

 
   ( 61 bytes / SIZE 005 )
 
 

STACK	INPUTS	OUTPUTS
Z	m	/
Y	n	/
X	r	T(m,n,r)

 
Example:

   2   SQRT
   3   SQRT
  PI   XEQ "TOR"  >>>>  T( sqrt(2),sqrt(3),PI ) = 0.963524225                ---Execution time = 26s---
 

Reference:

[1]   Abramowitz and Stegun - "Handbook of Mathematical Functions" -  Dover Publications -  ISBN  0-486-61272-4