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- W2040881468 abstract "Abstract Explicit evaluations of the symmetric Euler integral are obtained for some particular functions f . These evaluations are related to duplication formulae for Appell’s hypergeometric function F 1 which give reductions of F 1 ( α, β, β , 2 α, y, z ) in terms of more elementary functions for arbitrary β with z = y /( y − 1) and for β = α + 1/2 with arbitrary y, z . These duplication formulae generalize the evaluations of some symmetric Euler integrals implied by the following result: if a standard Brownian bridge is sampled at time 0, time 1, and at n independent randomtimes with uniformdistribution on [0, 1], then the broken line approximation to the bridge obtained from these n + 2 values has a total variation whose mean square is n ( n + 1)/(2 n + 1)." @default.
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- W2040881468 date "2000-10-01" @default.
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- W2040881468 title "Algebraic Evaluations of Some Euler Integrals, Duplication Formulae for Appell's Hypergeometric Function <i>F</i><sub>1</sub>, and Brownian Variations" @default.
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- W2040881468 doi "https://doi.org/10.4153/cjm-2000-040-3" @default.
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