Back to Search
Start Over
A Ramanujan integral and its derivatives: computation and analysis.
- Source :
-
Mathematics of Computation . May2024, Vol. 93 Issue 347, p1297-1308. 12p. - Publication Year :
- 2024
-
Abstract
- The principal tool of computation used in this paper is classical Gaussian quadrature on the interval [0,1], which happens to be particularly effective here. Explicit expressions are found for the derivatives of the Ramanujan integral in question, and it is proved that the latter is completely monotone on (0,\infty). As a byproduct, known series expansions for incomplete gamma functions are examined with regard to their convergence properties. The paper also pays attention to another famous integral, the Euler integral — better known as the gamma function — revitalizing a largely neglected part of the function, the part corresponding to negative values of the argument, which plays a prominent role in our work. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GAMMA functions
*INTEGRALS
*GAUSSIAN quadrature formulas
*EULER equations
Subjects
Details
- Language :
- English
- ISSN :
- 00255718
- Volume :
- 93
- Issue :
- 347
- Database :
- Academic Search Index
- Journal :
- Mathematics of Computation
- Publication Type :
- Academic Journal
- Accession number :
- 175630485
- Full Text :
- https://doi.org/10.1090/mcom/3892