(HP15C)(HP67)(HP41C) Bernoulli Polynomials

09012023, 11:53 AM
Post: #16




RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials
For B(16) using my program listed above in approximate mode (all floatingpoint numbers) I get exactly 7.1. The largest term in the 15th row of A163626 is ~10^14 so some rounding is inevitable, and would certainly be worse for 10digit calculators.
The largest row with all numbers < 10^10 is row 11 which should allow accurate computation of B(12). The value of B(12) to 12 digits is 0.253113553114, while the program returns 0.25312, which has only four correct digits. The exact value of B(12) is 691/2730 so we should expect more accurate results. Your idea of scaling the terms by their LCM is interesting but I can't see how one could compute the LCM on calculators limited to 10digit floats. 

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