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On some q-series identities related to a generalized divisor function and their implications

Gupta, Rajat; Kumar, Rahul (Cornell University Library, 2020-12)

n this article, a q-series examined by Kluyver and Uchimura is generalized. This allows us to find generalization of the identities in the random acyclic digraph studied by Simon, Crippa, and Collenberg in 1993. As one of ...
Lyapunov?type inequalities for singular elliptic partial differential equations

Kumar, Dharmendra; Tyagi, Jagmohan (Wiley, 2020-12)

We establish Lyapunov?type inequalities for a class of singular elliptic partial differential equations. As an application of Lyapunov?type inequalities, we obtain lower bounds for the first eigenvalue of the associated ...
A generalized modified Bessel function and explicit transformations of certain Lambert series

Dixit, Atul; Kesarwani, Aashita; Kumar, Rahul (Cornell University Library, 2020-12)

An exact transformation, which we call a \emph{master identity}, is obtained for the series ??n=1?a(n)e?ny for a?C and Re(y)>0. As corollaries when a is an odd integer, we derive the well-known transformations of the ...
Existence and uniqueness of weak solutions to parabolic problems with nonstandard growth and cross diffusion

Arumugam, Gurusamy; Erhardt, Andre H. (Department of Mathematics, 2020-12)

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