(HP15C)(HP67)(HP41C) Bernoulli Polynomials
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09-05-2023, 10:39 PM
Post: #26
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RE: (HP15C)(HP67)(HP41C) Bernoulli Polynomials
(09-05-2023 09:47 PM)John Keith Wrote: Of course, we then need a way to compute divisors of m and primes or GCD, which no HP calculator before the HP49 has. There are good factoring libraries for the HP-48 but this would not be easy for keystroke programmable calculators. We can use the fact that D = 2*(2^m-1) has all d factors. Also, d prime factors ≤ (m+1), relatively small number. Code: function ratioB(m) lua> for m=2,40,2 do print(m, ratioB(m)) end 2 1 6 4 -1 30 6 1 42 8 -1 30 10 5 66 12 -691 2730 14 7 6 16 -3617 510 18 43867 798 20 -174611 330 22 854513 138 24 -236364091 2730 26 8553103 6 28 -23749461029 870 30 8615841276005 14322 32 -7709321041217 510 34 2577687858367 6 36 -26315271553053516000 1919190 38 2929993913841563 6 40 -261082718496449660000 13530 Note that all B(m) denominator's are correct. IEEE double (53 bits) managed to get upto B(34) fraction exactly. |
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