The Museum of HP Calculators

Dawson's Integral for the HP-41

This program is supplied without representation or warranty of any kind. Jean-Marc Baillard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

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

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