(HP15C)(HP67)(HP41C) Bernoulli Polynomials
09-08-2023, 11:26 PM
Post: #28
 John Keith Senior Member Posts: 1,039 Joined: Dec 2013
RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials
Now that we have (mostly) conquered Bernoulli numbers, we can get back to the original purpose of this thread which is Bernoulli polynomials. Albert's second program in post #20 is simple and clearly written, and should be easy to implement on any HP calculator that can handle Bernoulli numbers.

To start off, here is an implementation that will run on any RPL calculator. In this example, BERN can refer to the first program in this post in the other thread, or the program here. In the latter case, BERN should be followed by / (divide).

Code:
 \<< \-> m x   \<< 1. 1. 1. m     FOR k m k - 1. + * k /       SWAP x * OVER k BERN * + SWAP     NEXT DROP   \>> \>>
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 Messages In This Thread (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Namir - 08-28-2023, 01:10 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 08-29-2023, 01:57 AM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 08-30-2023, 04:30 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 08-30-2023, 11:59 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - John Keith - 08-31-2023, 01:08 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 08-31-2023, 06:43 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 08-31-2023, 07:30 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Namir - 08-29-2023, 11:47 AM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 08-29-2023, 05:47 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 08-29-2023, 03:49 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 08-30-2023, 12:10 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Namir - 08-29-2023, 07:23 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 08-29-2023, 08:21 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - John Keith - 08-29-2023, 09:16 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Namir - 08-30-2023, 09:58 AM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - John Keith - 09-01-2023, 11:53 AM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 09-01-2023, 06:18 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 09-01-2023, 06:58 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 09-02-2023, 05:44 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - John Keith - 09-05-2023, 05:57 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 09-05-2023, 07:09 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 09-05-2023, 08:15 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 09-03-2023, 01:20 AM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Paul Dale - 09-03-2023, 05:35 AM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - John Keith - 09-05-2023, 09:47 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - Albert Chan - 09-05-2023, 10:39 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - John Keith - 09-07-2023, 04:31 PM RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials - John Keith - 09-08-2023 11:26 PM

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