Generalised Bernoulli function

[Parcly-Taxel]

This ticket implements in bernoulli_gen() the generalised Bernoulli function described in Peter Luschny's "An introduction to the Bernoulli function" (https://arxiv.org/abs/2009.06743):

B(s,x) = -s ζ(1-s,x) if s ≠ 0, 1 if s = 0

Arb PR: flintlib/arb#438

CC: @PeterLuschny @DavidAyotte

Component: number theory

Keywords: bernoulli transcendental function

Author: Jeremy Tan Jie Rui

Branch/Commit: u/gh-Parcly-Taxel/bernoulli @ c704e79

Issue created by migration from https://trac.sagemath.org/ticket/34536

[Parcly-Taxel]

Description changed:

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 This ticket implements in `bernoulli_gen()` the generalised Bernoulli function described in Peter Luschny's "An introduction to the Bernoulli function" (https://arxiv.org/abs/2009.06743):
 
 `B(s,x) = -s ζ(1-s,x) if s ≠ 0, 1 if s = 0`
+
+Arb PR: https://github.com/fredrik-johansson/arb/pull/438