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On differentiation with respect to parameters of the functions of the Mittag-Leffler type https://arxiv.org/abs/2408.05225 #mathGM

On differentiation with respect to parameters of the functions of the Mittag-Leffler type

The formal term-by-term differentiation with respect to parameters is demonstrated to be legitimate for the Mittag-Leffler type functions. The justification of differentiation formulas is made by using the concept of the uniform convergence. This approach is applied to the Mittag-Leffler function depending on two parameters and, additionally, for the 3-parametric Mittag-Leffler functions (namely, for the Prabhakar function and the Le Roy type functions), as well as for the 4-parametric Mittag-Leffler function (and, in particular, for theWright function). The differentiation with respect to the involved parameters is discussed also in case those special functions which are represented via the Mellin-Barnes integrals.

arxiv.org
August 14, 2024 at 3:10 AM · · feed2toot · 0 · 0 · 0
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