New Approximation Formula of Digamma Function with Bounded Remainder

Mansour Mahmoud (), Abdulaziz S. Alofi and Mohammed A. Zurayyir
Additional contact information
Mansour Mahmoud: Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Abdulaziz S. Alofi: Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Mohammed A. Zurayyir: Mathematics Department, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2025, vol. 13, issue 5, 1-12

Abstract: This study establishes the new approximation formula for the Digamma function ψ ( s ) = ln s − 1 2 s − 1 12 s s 2 + θ ( s ) , 1 36 < θ ( s ) < 1 5 ; s > 0 , as well as some of its inequalities, where θ ( s ) is a continuous function. We demonstrate numerically that our results are superior to some recent results.

Keywords: Digamma function; asymptotic expansion; approximation formula; inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/5/720/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/5/720/ (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:13:y:2025:i:5:p:720-:d:1597964

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 ().