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• W3017672123 abstract "In this work, properties of one- or two-parameter Mittag-Leffler functions are derived using the Laplace transform approach. It is demonstrated that manipulations with the pair direct–inverse transform makes it far more easy than previous methods to derive known and new properties of the Mittag-Leffler functions. Moreover, it is shown that sums of infinite series of the Mittag-Leffler functions can be expressed as convolution integrals, while the derivatives of the Mittag-Leffler functions with respect to their parameters are expressible as double convolution integrals. The derivatives can also be obtained from integral representations of the Mittag-Leffler functions. On the other hand, direct differentiation of the Mittag-Leffler functions with respect to parameters produces an infinite power series, whose coefficients are quotients of the digamma and gamma functions. Closed forms of these series can be derived when the parameters are set to be integers." @default.
• W3017672123 created "2020-05-01" @default.
• W3017672123 creator A5087105386 @default.
• W3017672123 date "2020-04-26" @default.
• W3017672123 modified "2023-10-14" @default.
• W3017672123 title "Differentiation of the Mittag-Leffler Functions with Respect to Parameters in the Laplace Transform Approach" @default.
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• W3017672123 doi "https://doi.org/10.3390/math8050657" @default.
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