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- W4254734501 abstract "We prove that the function [ {left ( {frac {b} {a}} right )^{mu - v}}frac {{{K_mu }(b{x^{1/2}}){K_v}(a{x^{1/2}})}} {{{K_mu }(a{x^{1/2}}){K_v}(b{x^{1/2}})}}] is the Laplace transform of an infinitely divisible probability distribution when $v > mu geqslant 0$ and $b > a > 0$. This implies the complete monotonic ity of the function. We also establish a representation as a Stieltjes transform, which implies in particular that the function has positive real part when $x$ lies in the right half-plane. We conjecture that [ {left ( {frac {b} {a}} right )^{mu - v}}frac {{{I_mu }(a{x^{1/2}}){I_v}(b{x^{1/2}})}} {{{I_mu }(b{x^{1/2}}){I_v}(a{x^{1/2}})}}] also is the Laplace transform of an infinitely divisible probability distribution. It is known that in the limit as $v to infty$, the infinite divisibility property holds for both functions." @default.
- W4254734501 created "2022-05-12" @default.
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- W4254734501 date "1982-06-01" @default.
- W4254734501 modified "2023-09-26" @default.
- W4254734501 title "An Infinitely Divisible Distribution Involving Modified Bessel Functions" @default.
- W4254734501 doi "https://doi.org/10.2307/2044288" @default.
- W4254734501 hasPublicationYear "1982" @default.
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