A \(q\)-Raabe formula and an integral of the fourth Jacobi theta function

DOI10.1016/j.jnt.2012.08.025zbMath1284.11135arXiv1106.1042OpenAlexW2067428091WikidataQ29394765 ScholiaQ29394765MaRDI QIDQ1930124

István Mezö

Publication date: 10 January 2013

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.1042

zbMATH Keywords

Riemann zeta functionpartition functionhypergeometric functionJacobi theta functionsRaabe-formulaq-Gamma functionq-Loggamma function

Mathematics Subject Classification ID

Analytic theory of partitions (11P82)

Related Items (4)

Cutting the Coon amplitude ⋮ Short proofs for \(q\)-Raabe formula and integrals for Jacobi theta functions ⋮ On \(q\)-Raabe integral and some extensions ⋮ Explicit evaluation of some quadratic Euler-type sums containing double-index harmonic numbers

Cites Work

• Generalized Lerch formulas: examples of zeta-regularized products
• The \(q\)-gamma function for \(q>1\)
• The q-gamma function for \(x<0\)
• Zeta regularizations
• Generalized zeta regularizations, quantum class number formulas, and Appell's \(O\)-functions
• Integrals of powers of loggamma
• PERIOD DEFORMATIONS AND RAABE'S FORMULAS FOR GENERALIZED GAMMA AND SINE FUNCTIONS
• Ramanujan's Extensions of the Gamma and Beta Functions
• Theq-Gamma andq-Beta Functions†
• On an Intriguing Integral and Some Series Related to ζ(4)
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