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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

Contributions to the Theory of the Barnes Function

classification math.CA math-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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    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. On the volume of the elliptope and related metric polytopes

    cs.DM 2026-04 unverdicted novelty 6.0

    Volume of rooted metric polytope exceeds that of elliptope on complete graphs, metric polytope volume is smaller than elliptope for small n but likely larger for big n, with exact cut polytope volumes for some sparse graphs.