Extensions of several summation formulae of Ramanujan using the calculus of residues

DOI10.1216/RMJ-1983-13-4-557zbMath0537.10007OpenAlexW1982359918MaRDI QIDQ792366

Peter J. Forrester

Publication date: 1983

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-1983-13-4-557

zbMATH Keywords

Riemann zeta-functionBernoulli numberBessel functionCauchy theoremRamanujan's formulaEpstein zeta- functionmultidimensional generalization of Lambert seriesRamanujan's summation formulae

Mathematics Subject Classification ID

Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Exponential sums and character sums (11L99)

Related Items (4)

Some integrals in Ramanujan’s lost notebook ⋮ Transformation of generalized multiple Riemann zeta type sums with repeated arguments ⋮ Closed expressions for some useful integrals involving Legendre functions and sum rules for zeroes of Bessel functions ⋮ On Taylor-like integral representations of analytic functions

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