(HP15C)(HP67)(HP41C) Bernoulli Polynomials

[Namir]

(08-29-2023 09:16 PM)John Keith Wrote:  The problem here is that all useful methods of calculating Bernoulli numbers involve fairly large numbers, and the classic hp's can only represent numbers < 10^10 exactly. Albert's method using Stirling numbers may be better than nested summation but will still see cancellation errors for n > 16.

One of my favorite methods uses Euler zigzag numbers. The numbers involved are smaller than factorials, and computing the zigzag numbers requires only addition. Also, this method requires only one division at the end, which prevents rounding errors from accumulating. However, i have not compared the two methods directly and there may be little or no improvement in practice.

Thanks John for the hint and the link. I am off today for a few weeks vacation in Europe (which kicks off with attending the wedding of a nephew in Greece!), so I may be slow in digesting the Euler Sizgzag numbers. They do look interesting!

Namir