Titlebook: Ramanujan Summation of Divergent Series; Bernard Candelpergher Book 2017 Springer International Publishing AG 2017 Ramanujan.Divergent.Ser

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書目名稱Ramanujan Summation of Divergent Series讀者反饋




書目名稱Ramanujan Summation of Divergent Series讀者反饋學(xué)科排名

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https://doi.org/10.1007/978-3-319-63630-6Ramanujan; Divergent; Series; Summation; Euler-MacLaurin formula; Borel Summation; Euler Summation

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Dependence on a Parameter,In this chapter we give three fundamental results on the Ramanujan summation of series depending on a parameter.

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Bernard CandelpergherProvides a clear and rigorous exposition of Ramanujan‘s theory of divergent series.A special chapter is devoted to an algebraic formalism unifying the most important summation processes.Only little ba

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Book 2017od, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical ev

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Ramanujan Summation,hird section we interpret this constant as the value of a precise solution of a difference equation. Then we can give in Sect.?. a rigorous definition of the Ramanujan summation and its relation to the usual summation for convergent series.