(HP15C)(HP67)(HP41C) Bernoulli Polynomials

[Namir]

A few weeks ago I published here a version of the HP-17B that evaluates Bernoulli polynomials. The BASIC code had a subroutine that calculates Bernoulli numbers and stores then in an array. The program allowed the user to repeatedly enter values for the polynomial order and for x. It remembers that last order used. If that is case, then it simply uses the current values in the Bernoulii numbers array.

I started thinking about using the same approach but realized the storage scheme is a bit quirky (and limited the order of the Bernoulli polynomials) since odd orders (except for 1) of the Bernoulli numbers are zero. When I saw the nested summation formula in Wikipedia, I decided that it would be an easier approach to code (albeit at the expense of some extra CPU time).

Namir