| dc.contributor.author |
Dixit, Atul |
|
| dc.contributor.author |
Kumar, Rahul |
|
| dc.coverage.spatial |
France |
|
| dc.date.accessioned |
2023-02-22T06:52:38Z |
|
| dc.date.available |
2023-02-22T06:52:38Z |
|
| dc.date.issued |
2023-02 |
|
| dc.identifier.citation |
Dixit, Atul and Kumar, Rahul, "A modular relation involving a generalized digamma function and asymptotics of some integrals containing Ξ(t)", Hardy-Ramanujan Journal, DOI: 10.46298/hrj.2023.10913, vol. 45, pp. 140-151, Feb. 2023. |
en_US |
| dc.identifier.issn |
2804-7370 |
|
| dc.identifier.uri |
https://doi.org/10.46298/hrj.2023.10913 |
|
| dc.identifier.uri |
https://repository.iitgn.ac.in/handle/123456789/8567 |
|
| dc.description.abstract |
A modular relation of the form F(α,w)=F(β,iw), where i=√−1and αβ=1, is obtained. It involves the generalized digamma function ψw(a) which was recently studied by the authors in their work on developing the theory of the generalized Hurwitz zeta function ζw(s,a). The limiting case w→0 of this modular relation is a famous result of Ramanujan on page 220 of the Lost Notebook. We also obtain asymptotic estimate of a general integral involving the Riemann function Ξ(t) as α→∞. Not only does it give the asymptotic estimate of the integral occurring in our modular relation as a corollary but also some known results. |
|
| dc.description.statementofresponsibility |
by Atul Dixit and Rahul Kumar |
|
| dc.format.extent |
vol. 45, pp. 140-151 |
|
| dc.language.iso |
en_US |
en_US |
| dc.publisher |
Episciences |
en_US |
| dc.subject |
Digamma function |
en_US |
| dc.subject |
Hurwitz zeta function |
en_US |
| dc.subject |
Lost notebook |
en_US |
| dc.subject |
Riemann function |
en_US |
| dc.subject |
Corollary |
en_US |
| dc.title |
A modular relation involving a generalized digamma function and asymptotics of some integrals containing Ξ(t) |
en_US |
| dc.type |
Journal Paper |
en_US |
| dc.relation.journal |
Hardy-Ramanujan Journal |
|