Dawson's Integral for the HP-41

Overview
 

-This program computes   F(x) = e ^{-x^2} §₀^x  e^{t^2} dt     by a series expansion.
   F(x) = e ^{-x^2} [ x + x³/3 + x⁵/(5 2!) + x⁷/(7 3!) + ..... ]
 

Program Listing
 

Data Registers: /
Flags: /
Subroutines: /
 
 

01  LBL "DAW" 02  STO M        03  X^2 04  STO N 05  1 06  LASTX

07  ENTER^ 08  LBL 01 09  CLX 10  RCL M        11  RCL N 12  *

13  R^ 14  ISG T 15  CLX 16  / 17  STO M        18  R^

19  ST+ X         20  DSE X 21  / 22  X<>Y 23  ST+ Y 24  X#Y?

25  GTO 01 26  RCL N        27  E^X 28  / 29  CLA 30  END

 
  ( 49 bytes / SIZE 000 )
 
 

STACK	INPUTS	OUTPUTS
X	x	F(x)
L	/	e x^2

 
Examples:

     1.94  XEQ "DAW"  >>>>  F( 1.94 ) =  0.3140571659     ( 11 seconds )
      10         R/S            >>>>    F(10)    =  0.05025384716   ( 85 seconds )
      15         R/S            >>>>    F(15)    =  0.03340790676     ( 2mn46s )

-For x > 15 , there will be an OUT OF RANGE.
 

Reference:

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