The Museum of HP Calculators

Debye Functions 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

-The following program computes db(x;n) = §_x^+infinity tⁿ/(e^t-1).dt where n is a positive integer and x > 0

Formula: db(x;n) = Sum_k>0 e^-k.x [ xⁿ/k + n.x^n-1/k² + ..... + n!/kⁿ⁺¹ ]

Program Listing

Data Registers: /
Flags: /
Subroutines: /

01 LBL "DEBYE"
02 CLA
03 STO M
04 X<>Y
05 STO N
06 CLST
07 LBL 01
08 R^
09 1
10 +
11 RCL M
12 RCL N
13 STO P ( synthetic )
14 Y^X
15 RCL Y
16 /
17 ENTER^
18 LBL 02
19 RCL P
20 *
21 R^
22 /
23 RCL M
24 /
25 ST+ Y
26 DSE P
27 GTO 02
28 X<> T
29 RCL M
30 *
31 E^X
32 /
33 RCL O
34 +
35 STO O
36 LASTX
37 X#Y?
38 GTO 01
39 RCL M
40 SIGN
41 X<> N
42 X<>Y
43 CLA
44 END

( 72 bytes / SIZE 000 )

      STACK        INPUTS      OUTPUTS

           Y             n             n

           X             x         db(x,n)

           L             /             x

n = a positive integer ; x > 0

Example:

3 ENTER^
0.7 XEQ "DEBYE" >>>> db( 0.7 ; 3 ) = 6.406833597 ( 55 seconds )

Note: We also have db(0;n) = §₀^+infinity tⁿ/(e^t-1).dt = n! Zeta(n+1) where "Zeta" is the Riemann Zeta Function.

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

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