Riemann-Siegel integral formula for the Lerch zeta function

DOI10.1090/S0025-5718-2011-02566-4zbMath1292.11097MaRDI QIDQ2840014

Jorge Sanchez Ortiz, Eugenio P. Balanzario

Publication date: 17 July 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

saddle pointLerch zeta functionRiemann-Siegel

Mathematics Subject Classification ID

Hurwitz and Lerch zeta functions (11M35) Analytic computations (11Y35)

Related Items (3)

Asymptotic behavior of the Lerch transcendent function ⋮ Some functional relations derived from the Lindelöf-Wirtinger expansion of the Lerch transcendent function ⋮ On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function

Uses Software

• goodwin.f77

Cites Work

• goodwin.f77
• A Riemann-Siegel formula for the Hurwitz zeta function
• Asymptotische Entwicklungen der Dirichletschen L-Reihen
• The Lerch zeta function I. Zeta integrals
• [https://portal.mardi4nfdi.de/wiki/Publication:3204019 The Evaluation of Integrals of the Form � +∞ -∞ f(t)exp(- t 2 ) dt: Application to Logistic-Normal Models]
• Error-Bounds for the Evaluation of Integrals by the Euler-Maclaurin Formula and by Gauss-Type Formulae
• A Method for the Calculation of the Zeta-Function
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