Prabhakar Functions of Le Roy Type: Inequalities and Asymptotic Formulae

Jordanka Paneva-Konovska ()
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Jordanka Paneva-Konovska: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

Mathematics, 2023, vol. 11, issue 17, 1-13

Abstract: In this paper, the four-index generalization of the classical Le Roy function is considered on a wider set of parameters and its order and type are given. Letting one of the parameters take non-negative integer values, a family of functions with such a type of index is constructed. The behaviour of these functions is studied in the complex plane C and in different domains thereof. First, several inequalities are obtained in C , and then they are modified on its compact subsets as well. Moreover, an asymptotic formula is proved for ‘large’ values of the indices of these functions. Additionally, the multi-index analogue of the abovementioned four-index Le Roy type function is considered and its basic properties are obtained. Finally, several special cases of the two functions under consideration are discussed.

Keywords: special functions; Le Roy function; Mittag-Leffler function; entire functions; inequalities; asymptotic formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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