(15C)Bessel Functions, Arbitrary Order for HP-15C

[Namir]

Bessel Function J, Arbitrary Order for HP-15C

Based on the HP-25 code by Peter Henrici in his book "Computational Analysis with the HP-25 Pocket Calculator", page 253. The pdf file for the book is available for download in Eric rechlin's librarry. The books shows the equations used and the flowchart for the program.

The program uses the following equations:

Jv(x) = a * sum((b(i)),for n= 0 to infinity

where,

a = (x/2)^v / gamma(v+1)
b(0) = 1
b(n) = -(x/2)^2/n/(v+n)*b(n-1) for n = 1, 2, 3, ...

The range for x values is 0<= x <= 10, according to Henrici.


Memory Map
==========

Code:

R0 = v
R1 = gamma(v+1)
R2 = 1e-12
R3 = a
R4 = sum
R5 = b
R6 = n
R7 = x/2

Program Listing
===============

Code:


01 LBL A
02 STO 0
03 X!
04 STO 1
05 X<>Y
06 2
07 /
08 STO 7
09 EEX
10 CHS
11 1
12 2
13 STO 2
14 RCL 7
15 RCL 0
16 Y^X
17 RCL 1
18 /
19 STO 3
20 1
21 STO 4
22 STO 5
23 STO 6
24 LBL 0
25 RCL 7
26 X^2
27 RCL 6
28 RCL 0
29 +
30 RCL 6
31 *
32 /
33 CHS
34 STO* 5
35 RCL 5
36 STO+ 4
37 ABS
38 RCL 2
39 X>=Y? (Test 9)
40 GTO 1
41 1
42 STO+ 6
43 GTO 0
44 LBL 1
45 RCL 3
46 RCL 4
47 *
48 RTN

Example
=======
To calculate J<1.5>(5), perform the following:

1) Set calculate to [FIX] [8].
2) Enter 5 (for x) and press [ENTER].
3) Enter the order of 1.5 and the press [f][A].
4) The program performs the calculations and stops displaying -0.16965131.