A one-parameter family of Pick functions defined by the Gamma function and related to the volume of the unit ball in $n$-space
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Publication:3005624
DOI10.1090/S0002-9939-2010-10636-6zbMath1230.30021OpenAlexW1990694513MaRDI QIDQ3005624
Christian Berg, Henrik Laurberg Pedersen
Publication date: 9 June 2011
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9939-2010-10636-6
Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Gamma, beta and polygamma functions (33B15) Asymptotic representations in the complex plane (30E15)
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Estimates of the function and quotient by Minc-Sathre ⋮ Topics in Special Functions III ⋮ Monotonicity and logarithmic convexity relating to the volume of the unit ball ⋮ Integral representations of bivariate complex geometric mean and their applications ⋮ Integral representations for multivariate logarithmic polynomials ⋮ A completely monotonic function used in an inequality of Alzer ⋮ Complete monotonicity of a function involving the ratio of gamma functions and applications ⋮ The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function ⋮ Inverses of Operator Convex Functions ⋮ Pick functions related to the triple gamma function ⋮ Delayed and rushed motions through time change ⋮ A ratio of finitely many gamma functions and its properties with applications ⋮ On applications of Herglotz-Nevanlinna functions in material sciences. I: Classical theory and applications of sum rules
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