(HP15C)(HP67)(HP41C) Bernoulli Polynomials

09052023, 05:57 PM
Post: #22




RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials
(09022023 05:44 PM)Albert Chan Wrote: We may be able to correct for tiny errors. B(m) largest denominator is 2*(2^m1). This is quite interesting, I haven't seen this method before. Can it be modified to avoid complex numbers so that it can be used on older and simpler calculators? Additionally, I have tested the method that I referred to above using zigzag (actually tangent) numbers, and the accuracy is far better than the method using Stirling numbers and factorials. On the HP48 (12 digits) the results are correct to all 12 digits up to B(18) and to 11 or 12 digits up to B(40), which is as far as I tested. Programs are here. Also see this paper for further information and algorithms. 

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