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Sums Involving the Digamma Function Connected to the Incomplete Beta Function and the Bessel functions.
- Source :
-
Mathematics (2227-7390) . Apr2023, Vol. 11 Issue 8, p1937. 16p. - Publication Year :
- 2023
-
Abstract
- We calculate some infinite sums containing the digamma function in closed form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as parameter differentiation formulas for the beta incomplete function, reduction formulas of 3 F 2 hypergeometric functions, or a definite integral which does not seem to be tabulated in the most common literature. As an application of certain sums involving the digamma function, we calculated some reduction formulas for the parameter differentiation of the Mittag–Leffler function and the Wright function. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BETA functions
*HYPERGEOMETRIC functions
*DEFINITE integrals
*BESSEL functions
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 11
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 163434128
- Full Text :
- https://doi.org/10.3390/math11081937