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Contributions to the Theory of the Barnes Function

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arxiv math/0308086 v1 pith:RFIDYFUS submitted 2003-08-08 math.CA math-phmath.MP

V.S.Adamchik This is my paper · ORCID
classification math.CAmath-phmath.MP
keywords functionbarnesgammaasymptoticcomputationconstantcontributionsdiscussed
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This paper presents a family of new integral representations and asymptotic series of the multiple gamma function. The numerical schemes for high-precision computation of the Barnes gamma function and Glaisher's constant are also discussed.

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Cited by 2 Pith papers

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  1. Eigenfunctions of deformed Schr\"odinger equations

    hep-th 2025-11 conditional novelty 7.0 of 10

    Explicit entire eigenfunctions are constructed for the difference operators 2Λ^N cosh(p)+V_N(x) with arbitrary polynomial potential; they become square-integrable only at a discrete set of energies.

  2. Refined Painlev\'e/gauge theory correspondence and quantum tau functions

    hep-th 2025-02 conditional novelty 6.0 of 10

    Strong-coupling expansions of N=2 SU(2) partition functions in general Omega-background are derived from quantum Painlevé equations obtained via C2/Z2 blowup relations, and match refined holomorphic anomaly and irregu...

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