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Integral form of Le Roy-type hypergeometric function

Definite integral expression is derived for the generalized Le Roy-type hypergeometric (alpha- Mittag-Leffler in other words) function F_{; ; p, q}; ; ; ^{; ; (alpha)}; ; , alpha>0 on the real axis. Its important corollaries are the one-parameter, the two-parameter Mittag-Leffler function's and the CoM-Poisson normalization constant's integral forms.

Le Roy-type hypergeometric function ; Mittag-Leffler functions ; CoM-Poisson renormalization constant Z(lambda, nu) ; alpha L-exponential function ; Cahen integral ; Dirichlet series

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