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- W2009937194 abstract "The weighted power mean of two positive variables is strictly totally positive (STP) if its order t satisfies $ - infty < t < 0$, and its reciprocal is STP if $0 < t < infty $. The reciprocals of the logarithmic mean, Gauss’s arithmetic-geometric mean, and the Schwab–Borchardt mean are STP. The hypergeometric R-function $R_{ - alpha } (beta ,beta ':x,y),x,y > 0$, which is equivalent to ${}_2 F_1 $ with argument ${{1 - x} / y}$, is STP if $alpha ,beta beta '$, and $beta + beta ' - alpha $ are positive. With weaker restrictions this function is represented in a new way as a convolution. Higher order positivity is discussed for some other hypergeometric functions, including incomplete elliptic integrals." @default.
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- W2009937194 date "1983-03-01" @default.
- W2009937194 modified "2023-09-30" @default.
- W2009937194 title "Total Positivity of Mean Values and Hypergeometric Functions" @default.
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