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M. Aslam Chaudhry

Publications and source records attributed to M. Aslam Chaudhry.

5 recordsLinked to original sources
arXiv2010

Extended Fermi-Dirac and Bose-Einstein functions with applications to the family of zeta functions

Fermi-Dirac and Bose-Einstein integral functions are of importance not only in quantum statistics but for their mathematical properties, in themselves. Here, we have extended these functions by introducing an extra parameter in a way that gives new insights into these functions and their relation to the family of zeta functions. These extensions are "dual" to each other in a sense that is explained. Some identities are proved for them and the relation between them and the general Hurwitz-Lerch zeta function (ϕ(z,s,v) is exploited to deduce new identities.

math-ph↗
arXiv2010

A proof of Lindelöf's hypothesis

We define an associated Lindelöf-function for the ratio of the zeta functions and use its representation to get a unique extension of Lindelöf's function that proves Lindelöf's hypothesis.

math.GM↗
arXiv2005

A Representation for the Anyon Integral Function

The Fermi-Dirac and Bose-Einstein particles satisfy corresponding statistical distributions. In the phenomena of charge fractionalization and the fractional quantum Hall effect it is found that particles behave as if they are neither fermions nor bosons. Such particles are called anyons. The integral functions for bosons and fermions are available in the literature. However, there is no anyon integral function available. In this note we propose a pair of functions that interpolate, in some sense, between the gamma function and the zeta function, which we call "gamma-zeta" functions. It is pointed out that this pair of functions very naturally provides a representation of the anyon integral function.

math-ph↗
arXiv1998

Transformation of the extended Gamma function $Γ^{2,0}_{0,2}[(b,x)]$ with applications to astrophysical thermonuclear functions

Two representations of the extended gamma functions $Γ^{2,0}_{0,2}[(b,x)]$ are proved. These representations are exploited to find a transformation relation between two Fox's $H$-functions. These results are used to solve Fox's $H$-function in terms of Meijer's $G$-function for certain values of the parameters. A closed form representation of the kernel of the Bessel type integral transform is also proved.

astro-ph↗