Theta Functions for the HP-41
Overview
Definitions: with q = e-pi K'/K ( see Jacobian elliptic functions for the HP-41 )
Theta1(x;q) = 2.q1/4 SUMk>=0
(-1)k qk(k+1) sin(2k+1)x
Theta2(x;q) = 2.q1/4 SUMk>=0
qk(k+1) cos(2k+1)x
Theta3(x;q) = 1 + 2 SUMk>=1
qk*k cos 2kx
( -1 < q < 1 )
Theta4(x;q) = 1 + 2 SUMk>=1 (-1)k
qk*k cos 2kx
Program Listing
Data Registers: R00-R03: temp R01 =
x R02 = q
Flags: F01 , F02 , F03 , F04
Set
only one of these 4 Flags
Subroutines: /
-If flag F01 is set , "THETA" calculates Theta1(x;q)
-If flag F02 is set , "THETA" calculates Theta2(x;q)
-If flag F03 is set , "THETA" calculates Theta3(x;q)
-If flag F04 is set , "THETA" calculates Theta4(x;q)
-Synthetic registers M , N , O may be replaced by any unused data registers.
| 01 LBL "THETA"
02 STO 01 03 10 04 CHS 05 RCL Z 06 STO 02 07 ABS 08 X#0? 09 LOG 10 X#0? 11 / 12 SQRT 13 INT 14 STO 00 15 1 16 FC? 01 |
17 FS? 04
18 CHS 19 X<>Y 20 Y^X 21 STO 03 22 CLX 23 RAD 24 ISG 00 25 LBL 01 26 RCL 02 27 RCL 00 28 ENTER 29 ST* Y 30 FC? 03 31 FS? 04 32 CLX |
33 +
34 Y^X 35 RCL 03 36 FC? 01 37 FS? 04 38 CHS 39 STO 03 40 * 41 RCL 00 42 ST+ X 43 RCL 01 44 ST* Y 45 FC? 03 46 FS? 04 47 CLX 48 + |
49 FS? 01
50 SIN 51 FC? 01 52 COS 53 * 54 + 55 DSE 00 56 GTO 01 57 FC? 01 58 FS? 02 59 RCL 01 60 FS? 01 61 SIN 62 FS? 02 63 COS |
64 DEG
65 FC? 03 66 FS? 04 67 .5 68 + 69 ST+ X 70 RCL 02 71 ABS 72 SQRT 73 SQRT 74 FC? 03 75 FS? 04 76 SIGN 77 * 78 END |
( 116 bytes / SIZE 004 )
| STACK | INPUTS | OUTPUTS |
| Y | q | / |
| X | x | Thetan (x,q) |
Example: Compute Theta1(x,q) , Theta2(x,q)
, Theta3(x,q) , Theta4(x,q) for x = 2 , q = 0.3
- CF02 CF 03 CF 04
- SF 01
0.3 ENTER^ 2 XEQ "THETA" gives
1.382545289
---Execution time = 10s---
- CF01 SF 02 0.3 ENTER^
2 R/S
gives -0.488962527
- CF 02 SF 03 0.3 ENTER^
2 R/S
gives 0.605489938
idem
- CF 03 SF 04 0.3 ENTER^
2 R/S
gives 1.389795845
Reference:
[1] Abramowitz and Stegun , "Handbook of Mathematical Functions"
- Dover Publications - ISBN 0-486-61272-4