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+--- Thread: Zeta Function (/thread-5559.html)
Zeta Function - Namir - 01-19-2016 09:57 PM
Here is a program that calculates the Zeta function. The program prompts you for s, the argument for the function, and for the tolerance value (recommend 1e-8). The function places the function's value in the X stack register,
Code:
1 LBL "ZETA"
2 LBL A
3 S?
4 PROMPT
5 STO 0
6 TOLER?
7 PROMPT
8 STO 07 # store tolerance
9 1
10 STO 04 # n=1
11 STO 08 # n! = 1
12 2
13 /
14 STO 01 # OutSum = 1/2
15 LBL 00 #--------------------------- start of outer loop
16 RCL 04 # View n
17 PSE
18 STO 11 # I = n
19 STO* 08 # update n!
20 RCL 08
21 STO 10 # init (n-k)!
22 1
23 STO 03 # k = 1
24 STO 09 # k! =1
25 STO 02 # InSum = 1
26 STO 06 # CHS=1
27 LBL 01 # --------------------------- start of inner loop
28 -1
29 STO* 06 # CHS=-CHS
30 RCL 03
31 STO* 09 # update k!
32 RCL 11
33 X=0?
34 GTO 02
35 STO/ 10 # update (n-k)!
36 1
37 RCL 10
38 X=0?
39 +
40 STO 10
41 1
42 STO- 11 # I = I - 1
43 LBL 02
44 RCL 08
45 RCL 09
46 /
47 RCL 10
48 /
49 RCL 06
50 *
51 RCL 03
52 1
53 +
54 STO 03 # k = k + 1
55 RCL 00
56 Y^X
57 /
58 STO+ 02 # InSum = InSum + ...
59 RCL 04
60 RCL 03
61 X<=Y? # k<=n?
62 GTO 01 # --------------------------- End of Inner loop
63 RCL 02
64 2
65 RCL 04
66 1
67 +
68 STO 04 # n = n + 1
69 +
70 Y^X
71 /
72 STO+ 01 # OutSum = OutSum + Term
73 ABS
74 RCL 07
75 X<=Y? # Tolerance <= Term?
76 GTO 00 # --------------------------- End of Outer loop
77 2
78 1
79 RCL 00
80 -
81 Y^X
82 CHS
83 1
84 + # calculate 1 - 2^(1-s)
85 1/X
86 RCL 01
87 *
88 RTNThe memory map for the program is:
Code:
R00 = s
R01 = Outer Sun, Outer Sum
R02 = Inner Sum, Inner Sum
R03 = k
R04 = n
R05 = Term
R06 = CHS
R07 = Toler
R08 = n!
R09 = k!
R10 = (n-k)!
R11 = IThe function uses a fast converging series (see Wikipedia) and can give results for small arguments of s such as Zeta(1.1).
Namir
PS: I am aware that Jean-Marie Baillard has a Zeta function implemented in the HP-41C Software Library. His program is shorter than mine and uses just two registers. However, I tried to calculate Zeta(1.1) using his version and I had to stop after the HP-41CX emulator went on and on and on!
RE: Zeta Function - Ángel Martin - 01-24-2016 09:25 AM
(01-19-2016 09:57 PM)Namir Wrote: PS: I am aware that Jean-Marie Baillard has a Zeta function implemented in the HP-41C Software Library. His program is shorter than mine and uses just two registers. However, I tried to calculate Zeta(1.1) using his version and I had to stop after the HP-41CX emulator went on and on and on!
Hi Namir, I guess you must have something wrong in your V41 setup - or a bad transcription of the program code. I just ran the case x=1.1 using ZETAX in the SandMath (which implements Jean-Marc's Borwein algorithm) and it took 13.48 seconds to return the result 10.58444847. I also ran it for x=1.001, which returned 1,000.577289 in approximately the same time. Both examples done at the default speed, i.e. NOT in TURBO mode.
Cheers,
'AM