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Convexity in the Theory of the Gamma Function

Milan Merkle

Abstract


Convexity is a fundamental property of the Gamma function, as shown by pioneering work of Emil Artin, Wolfgang Krull and others. We start with revisiting Krull’s work about the functional equation f(x + 1) − f(x) = g(x), in a more modern presentation and a slightly more general setup. We present applications of these results to deriving classical and new expansions, respresentations and characterizations of the Gamma function.

Keywords


Functional equation, Gamma function, convexity.

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