(12C+) Bernoulli Number
07-27-2019, 06:41 AM (This post was last modified: 07-28-2019 06:08 AM by Gamo.)
Post: #1
 Gamo Senior Member Posts: 713 Joined: Dec 2016
(12C+) Bernoulli Number
In need of the Bernoulli Number using HP-12C ?

Here is an attempt to generate a Bernoulli Number constant using 12C

Without a Pi function this program use 355/113 which give out about

4 to 5 digits precision.

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To run:
If you need to know B10 divide it by 2 is 5

5 [R/S] display 0.07576 [R/S] 5 [X<>Y] 66

Answer: B10 is 0.07576 or in fraction is 5/66
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B12

12 ÷ 2 = 6

6 [R/S] display 0.25311 [R/S] 61 [X<>Y] 241

B12 since 12 is divisible by 4 answer is Negative

-0.25311 in fraction is -61/241
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Remark:
To find B(n) divide it by 2 and calculate.
This program do not give answer of the alternate negative value
such as B2 = 1/6 where B4 = -1/30
For B(n) that divisible by 4 answer is "Negative"
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Program:
Code:
 2 x STO 2 355 ENTER 113 ÷ STO 3 1 STO 0 STO 1 ----------------- RCL 0  // line 16 2 x 1 + RCL 2 CHS Y^X RCL 1 + RCL 1 X<>Y X≤Y GTO 34 STO 1 1 STO+0 GTO 16 RCL 2  // Line 34 n! 2 x RCL 1 x 2 RCL 2 Y^X 1 - RCL 2 RCL 3 X<>Y Y^X x ÷  // B(n) constant end here ---------------- R/S  // Line 51 STO 0  // Decimal to Fraction start here STO 1 0 STO 2 1 RCL 0 INTG  // Line 58 RCL 2 x + STO 2 RCL 0 x . 5 // decimal and five // Line 66 + INTG STO 3 RCL 2 ÷ RND RCL 0 RND -  // Subtract sign X=0 GTO 86 Rv  // Roll Down RCL 2 X<>Y RCL 1 FRAC 1/x STO 1 GTO 58 RCL 2  // Line 86 RCL 3 GTO 00  // Line 88

Formula use to calculate Bernoulli Number

B(n) = [2(2n)! ÷ ((2^2n) - 1)(Pi^2n)] [1 + (1/3^2n) + (1/5^2n) + ...]

Gamo
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 Messages In This Thread (12C+) Bernoulli Number - Gamo - 07-27-2019 06:41 AM RE: (12C+) Bernoulli Number - Albert Chan - 07-27-2019, 12:41 PM RE: (12C+) Bernoulli Number - Gamo - 07-27-2019, 01:40 PM RE: (12C+) Bernoulli Number - John Keith - 07-27-2019, 07:49 PM RE: (12C+) Bernoulli Number - Albert Chan - 07-28-2019, 12:02 AM RE: (12C+) Bernoulli Number - John Keith - 07-28-2019, 11:21 AM RE: (12C+) Bernoulli Number - Albert Chan - 07-28-2019, 01:08 AM RE: (12C+) Bernoulli Number - Gamo - 07-28-2019, 02:29 AM RE: (12C+) Bernoulli Number - Albert Chan - 07-31-2019, 05:14 PM

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