Zur Entwicklungsgeschichte derEulerschen Summenformel

Hofmann, Joseph Ehrenfried

doi:10.1007/bf01258851

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Euler's Work1

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2013

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“…For discussions of Euler's early work up to 1750 see Sandifer [266], [267]. For his work on the Euler(-Maclaurin) summation formula see Hofmann [167] and Knoebel et al [178,Chapter 1]. For other discussions of his work on the zeta function see Stäckel [285], Ayoub [21], Weil [315,Chap.…”

Section: Euler's Workmentioning

confidence: 99%

Euler’s constant: Euler’s work and modern developments

Lagarias

2013

Bull. Amer. Math. Soc.

127

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Abstract. This paper has two parts. The first part surveys Euler's work on the constant γ = 0.57721 · · · bearing his name, together with some of his related work on the gamma function, values of the zeta function, and divergent series. The second part describes various mathematical developments involving Euler's constant, as well as another constant, the Euler-Gompertz constant. These developments include connections with arithmetic functions and the Riemann hypothesis, and with sieve methods, random permutations, and random matrix products. It also includes recent results on Diophantine approximation and transcendence related to Euler's constant.

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