Double and Single Integrals of the Mittag-Leffler Function: Derivation and Evaluation
DOI:
https://doi.org/10.62298/advmath.24Keywords:
Mittag-Leffler function, Double integral, Cauchy integral, Hypergeometric functionAbstract
One-dimensional and two-dimensional integrals containing Eb(−u) and Eα,β (δxγ) are considered. Eb(−u) is the Mittag-Leffler function and the integral is taken over the rectangle 0 ≤ x < ∞, 0 ≤ u < ∞ and Eα,β (δxγ) is the generalized Mittag-Leffler function and the integral is over 0 ≤ x ≤ b with infinite intervals explored. A representation in terms of the Hurwitz-Lerch zeta function and other special functions are derived for the double and single integrals, from which special cases can be evaluated in terms of special function and fundamental constants.
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