Titlebook: Bernoulli Numbers and Zeta Functions; Tsuneo Arakawa,Tomoyoshi Ibukiyama,Masanobu Kaneko Book 2014 Springer Japan 2014 Bernoulli numbers a

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https://doi.org/10.1007/978-0-387-72577-2In this chapter, we introduce Barnes’ multiple zeta function, which is a natural generalization of the Hurwitz zeta function, give an analytic continuation, and then express their special values at negative integers by using Bernoulli polynomials.

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,The Euler–Maclaurin Summation Formula and the Riemann Zeta Function,In this chapter we give a formula that describes Bernoulli numbers in terms of Stirling numbers. This formula will be used to prove a theorem of Clausen and von Staudtin the next chapter. As an application of this formula, we also introduce an interesting algorithm to compute Bernoulli numbers.

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ambivalence

Hurwitz Numbers,In this section, we briefly introduce Hurwitz’s Hurwitz generalization of Bernoulli numbers, known as the Hurwitz numbers.