Krull’s theory for the double gamma function |
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| Authors: | Milan Merkle Monica Moulin Ribeiro Merkle |
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| Affiliation: | a Department of Mathematics, Faculty of Electrical Engineering, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia
b Institute of Mathematics, Federal University of Rio de Janeiro, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ, Brazil |
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| Abstract: | The Barnes’ G-function G(x) = 1/Γ2, satisfies the functional equation logG(x + 1) − logG(x) = logΓ(x). We complement W. Krull’s work in Bemerkungen zur Differenzengleichung g(x + 1) − g(x) = φ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on x > 0 in terms of Gamma and Digamma functions, a new expansion for the Gamma function and summation formulae with Polygamma functions. |
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| Keywords: | Barnes&rsquo G-function Krull&rsquo s functional equation Convexity |
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