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• W2786507831 abstract "A comprehensive study of the generalized Lambert series $displaystylesum_{n=1}^{infty}frac{n^{N-2h}exp{(-an^{N}x)}}{1-exp{(-n^{N}x)}}, 0 0$, $Ninmathbb{N}$ and $hinmathbb{Z}$, is undertaken. Two of the general transformations of this series that we obtain here lead to two-parameter generalizations of Ramanujan's famous formula for $zeta(2m+1)$, $m>0$ and the transformation formula for $logeta(z)$. Numerous important special cases of our transformations are derived. An identity relating $zeta(2N+1), zeta(4N+1),cdots, zeta(2Nm+1)$ is obtained for $N$ odd and $minmathbb{N}$. Certain transcendence results of Zudilin- and Rivoal-type are obtained for odd zeta values and generalized Lambert series. A criterion for transcendence of $zeta(2m+1)$ and a Zudilin-type result on irrationality of Euler's constant $gamma$ are also given. New results analogous to those of Ramanujan and Klusch for $N$ even, and a transcendence result involving $zetaleft(2m+1-frac{1}{N}right)$, are obtained." @default.
• W2786507831 created "2018-02-23" @default.
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• W2786507831 date "2018-01-28" @default.
• W2786507831 modified "2023-09-27" @default.
• W2786507831 title "Generalized Lambert series, Raabe's integral and a two-parameter generalization of Ramanujan's formula for ζ(2m+1)" @default.
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• W2786507831 hasPublicationYear "2018" @default.
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