Certain Unified Infinite Integrals Involving Incomplete Special Functions

• Published in: International journal of applied and computational mathematics Vol. 11; no. 5
• Main Authors: Kumar, Dinesh, Ayant, Frédéric, Sachan, Dheerandra Shanker
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.10.2025; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Science and Engineering; Infinite integrals; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Theoretical; Incomplete Aleph-function; Incomplete Gamma function; 33C60; Mellin–Barnes contour integrals; Infinite integral; 33C05
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-02013-6

Integrals have a variety of applications in many different areas like mathematics, science, engineering, statistics and economics. Keeping this fact in view, in this investigation, we evaluate some interesting general unified infinite integrals associated with incomplete Aleph-functions by using a known integral, which are expressed in terms of incomplete Aleph-functions. Next, we give some corollaries in terms of other incomplete special functions by assigning some particular values to the parameters of incomplete Aleph-functions (for example, incomplete I -function, incomplete H -function). The results presented in this paper are unified and general in nature.