Sums of Powers, Bernoulli Numbers, and the Gamma Function

Bruce C. Berndt
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Bruce C. Berndt: University of Illinois, Department of Mathematics

Chapter Chapter 7 in Ramanujan’s Notebooks, 1985, pp 150-180 from Springer

Abstract: Abstract The principal topics in Chapter 7 concern sums of powers, an extended definition of Bernoulli numbers, the Riemann zeta-function ζ(s) and allied functions, Ramanujan’s theory of divergent series, and the gamma function. This chapter thus represents a continuation of the subject matter of Chapters 5 and 6. Perhaps more so than any other chapter in the second notebook, Chapter 7 offers a considerable amount of numerical calculation. The extent of Ramanujan’s calculations is amazing, since he evidently performed them without the aid of a mechanical or electrical device.

Keywords: Positive Integer; Complex Number; Analytic Continuation; Gamma Function; Decimal Place (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-1-4612-1088-7_8

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