Sums Involving the Digamma Function Connected to the Incomplete Beta Function and the Bessel functions

Juan Luis González-Santander and Fernando Sánchez Lasheras ()
Additional contact information
Juan Luis González-Santander: Department of Mathematics, Universidad de Oviedo, 33007 Oviedo, Asturias, Spain
Fernando Sánchez Lasheras: Department of Mathematics, Universidad de Oviedo, 33007 Oviedo, Asturias, Spain

Mathematics, 2023, vol. 11, issue 8, 1-16

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.

Keywords: digamma function; Bessel functions; incomplete beta function; Wright function; Mittag–Leffler function; differentiation with respect to parameters (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)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/8/1937/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/8/1937/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:8:p:1937-:d:1128129

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().