5 papers
A modular relation involving a generalized digamma function and asymptotics of some integrals containing
Atul Dixit, Rahul Kumar
A modular relation of the form , where and , is obtained. It involves the generalized digamma function which was recently studied by…
Applications of Lipschitz summation formula and a generalization of Raabe's cosine transform
Atul Dixit, Rahul Kumar
General summation formulas have been proved to be very useful in analysis, number theory and other branches of mathematics. The Lipschitz summation formula is one of them. In this…
Extended Higher Herglotz function \textup{II}
Rajat Gupta, Rahul Kumar
Very recently, Radchenko and Zagier revived the theory of Herglotz functions. The main goal of the article is to show that one of the formulas on page 220 of Ramanujan's Lost Noteb…
On some -series identities related to a generalized divisor function and their implications
Rajat Gupta, Rahul Kumar
In this article, a -series examined by Kluyver and Uchimura is generalized. This allows us to find generalization of the identities in the random acyclic digraph studied by Simo…
Explicit transformations of certain Lambert series
Atul Dixit, Aashita Kesarwani, Rahul Kumar
An exact transformation, which we call the \emph{master identity}, is obtained for the first time for the series for and Re$(y…