On the confluent hypergeometric function coming from the Pareto distribution
نویسنده
چکیده
Making use of the confluent hypergeometric function we can obtain the Laplace-Stieltje transform of the Pareto distribution in the following form ζ(s) = hU(1; 1− h; s) = 1F1(1; 1− h; s)− Γ(1− h)s1F1(1 + h; 1 + h; s). About this transform, we obtain an identity, Γ(1 + h)|U(1, 1− h, s)|2 = ∫ ∞ 0 ∫ ∞ 0 λhe−λ−y |λ+ s|2 + λy 2000 Mathematical Subject Classification: 33C15, 60E07
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