Integrals of \(K\) and \(E\) from lattice sums

DOI10.1007/s11139-015-9710-zzbMath1412.11094arXiv1410.7081OpenAlexW2172168998MaRDI QIDQ282985

I. J. Zucker, James G. Wan

Publication date: 13 May 2016

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.7081

zbMATH Keywords

Mellin transformgamma functionhypergeometric seriesDirichlet \(L\)-seriescomplete elliptic integralJacobi theta functionlattice sum

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Modular and automorphic functions (11F03) Generalized hypergeometric series, ({}_pF_q) (33C20) Elliptic functions and integrals (33E05) Elliptic integrals as hypergeometric functions (33C75)

Related Items (4)

Ramanujan series for Epstein zeta functions ⋮ New Clebsch–Gordan‐type integrals involving threefold products of complete elliptic integrals ⋮ Two definite integrals involving products of four Legendre functions ⋮ Moments in Pearson's four-step uniform random walk problem and other applications of very well-poised generalized hypergeometric series

Cites Work

• Identities for the Ramanujan zeta function
• Legendre functions, spherical rotations, and multiple elliptic integrals
• Moments of products of elliptic integrals
• 70+ years of the Watson integrals
• On some integrals over the product of three Legendre functions
• Moments of elliptic integrals and critical \(L\)-values
• The Mahler measure of a Calabi-Yau threefold and special \(L\)-values
• Elliptic integral evaluations of Bessel moments and applications
• Three-Step and Four-Step Random Walk Integrals
• Lattice Sums Then and Now
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