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• W2042874672 abstract "It is shown that some new and some already known positivity results for integrals of Bessel functions and for generalized hypergeometric functions can be easily obtained by writing the integrals and functions either as a sum of squares of Bessel functions with positive coefficients or as a fractional integral of such a sum. In particular, this method is used to prove that $int_0^x {(x - t)^lambda t^{lambda + {1 / 2}} J_alpha (t)dt > 0,quad 0 leqq lambda leqq alpha - {1 / 2},quad alpha > 1/2, quad x > 0,} $ and to give a simple proof of Steinig’s recent result that the Lommel function $S_{mu ,nu } (x) > 0$ for $x > 0$ if, $mu = {1 / 2}$ and $ - {1 / 2} < nu < {1 / 2}$, or if $mu > {1 / 2}$ and $ - mu leqq nu leqq mu $." @default.
• W2042874672 created "2016-06-24" @default.
• W2042874672 creator A5074615747 @default.
• W2042874672 date "1975-10-01" @default.
• W2042874672 modified "2023-09-25" @default.
• W2042874672 title "Positive Integrals of Bessel Functions" @default.
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• W2042874672 doi "https://doi.org/10.1137/0506076" @default.
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