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Extensions of an Euler's Integral Through Statistical Techniques
Author(s) -
Mathai A. M.,
Saxena R. K.
Publication year - 1971
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19710510102
Subject(s) - mathematics , equating , euler's formula , product (mathematics) , moment (physics) , algebraic number , sequence (biology) , function (biology) , euler number (physics) , pure mathematics , mathematical analysis , euler equations , backward euler method , statistics , semi implicit euler method , geometry , physics , classical mechanics , evolutionary biology , biology , rasch model , genetics
Extensions of the Euler's integral ([4], p. 59 (10)) are given in this article. A statistical technique is used to derive the results. The exact density of a product of n stochastically independent Beta variates is obtained through two different methods, namely, through algebraic trans formations and through a moment sequence. From the unique existence of the density function, a number of results are obtained by equating the density obtained by the two methods. The technique developed in this article can be used in other situations as well.