(50g) Bernoulli polynomials
12-17-2018, 09:17 PM
Post: #5
 ttw Member Posts: 250 Joined: Jun 2014
RE: (50g) Bernoulli polynomials
There are some direct formulas without integrations (although I always use integration because it's non-numerical and easier to remember.)

B_m(X) = Sum(n:0:m)[1/(n+1)Sum(k:0:n)[(-1)^k*C(n,k)*(x+k)^m]

It's easier to start with 1 and integrate then scale the leading coefficient to 1 and add the constant to get the average to be zero. That's probably equivalent to what you are doing. It can all be done symbolically.

It's useful for periodizing functions before doing some types of integrations. The results are much "smoother" (fewer high frequency left over terms) than most periodization methods.
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 Messages In This Thread (50g) Bernoulli polynomials - peacecalc - 12-17-2018, 05:31 PM RE: (50g) Bernoulli polynomials - DavidM - 12-17-2018, 06:07 PM RE: (50g) Bernoulli polynomials - John Keith - 12-17-2018, 07:03 PM RE: (50g) Bernoulli polynomials - DavidM - 12-17-2018, 08:37 PM RE: (50g) Bernoulli polynomials - ttw - 12-17-2018 09:17 PM RE: (50g) Bernoulli polynomials - peacecalc - 12-17-2018, 10:03 PM RE: (50g) Bernoulli polynomials - ijabbott - 12-17-2018, 11:58 PM RE: (50g) Bernoulli polynomials - peacecalc - 12-22-2018, 11:06 PM RE: (50g) Bernoulli polynomials - John Keith - 12-23-2018, 07:58 PM RE: (50g) Bernoulli polynomials - peacecalc - 12-29-2018, 02:18 PM RE: (50g) Bernoulli polynomials - Albert Chan - 12-29-2018, 03:52 PM RE: (50g) Bernoulli polynomials - DavidM - 12-29-2018, 04:40 PM RE: (50g) Bernoulli polynomials - John Keith - 12-29-2018, 05:54 PM RE: (50g) Bernoulli polynomials - peacecalc - 12-30-2018, 01:44 PM RE: (50g) Bernoulli polynomials - ttw - 01-02-2019, 11:13 PM RE: (50g) Bernoulli polynomials - peacecalc - 01-03-2019, 10:20 AM

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