A Probabilistic Proof of Ramanujan’s ${}_1 \psi _1 $ Sum

DOI10.1137/0518110zbMath0638.62011OpenAlexW1978862030MaRDI QIDQ3779573

Kevin W. J. Kadell

Publication date: 1987

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0518110

zbMATH Keywords

order statisticsF distributiondiscrete distributionsMann-Whitney statisticbeta distributionbeta integralGaussian polynomialq-gamma functionq-binomial theoremq-chi-squared distributionq-F distributionRamanujan's psi-sum

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Exact enumeration problems, generating functions (05A15) Gamma, beta and polygamma functions (33B15) Characterization and structure theory of statistical distributions (62E10) Classical hypergeometric functions, ({}_2F_1) (33C05)

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