## Abstract

Derivatives with respect to the parameters of the integral Mittag-Leffler function and the integral Wright function, recently introduced by us, are calculated. These derivatives can be expressed in the form of infinite sums of quotients of the digamma and gamma functions. In some particular cases, these infinite sums are calculated in closed-form with the help of MATHEMATICA. However, parameter differentiation reduction formulas are explicitly derived in order to check some of the results given by MATHEMATICA, as well as to provide many other new results. In addition, we present these infinite sums graphically for particular values of the parameters. Finally, new results for parameter derivatives of the Mittag-Leffler and Wright functions are reported in the Appendices.

Original language | English |
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Pages (from-to) | 567-598 |

Number of pages | 32 |

Journal | Fractional Calculus and Applied Analysis |

Volume | 26 |

Issue number | 2 |

DOIs | |

State | Published - 1 Apr 2023 |

## Keywords

- Derivative with respect to parameters
- Integral Mittag-Leffler function
- Integral Wright function

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics