




Volume 28 • Number 2 • 2005 


•
Some Integral Properties of a General Class of Polynomials Associated
with Feynman Integrals
V.B.L. Chaurasia and Ashok Singh Shekhawat
Abstract.
The object of the present paper is to discuss certain integral
properties of a general class of polynomials and the Hfunction,
proposed by InayatHussain which contain a certain class of Feynman
integrals, the exact partition of a Gaussian model in statistical
mechanics and several other functions as its particular cases. During
the course of finding, we establish certain new double integral
relations pertaining to a product involving a general class of
polynomials and the Hfunction. These double integral relations
are unified in nature and act as a key formulae from which we can obtain
as their special cases, double integral relations concerning a large
number of simpler special functions and polynomials. For the sake of
illustration, we record here some special cases of our main results
which are also new and of interest by themselves. The results
established here are basic in nature and are likely to find useful
applications in several fields notably electrical networks, probability
theory and statistical mechanics.
2000
Mathematics Subject Classification: 33C60, 26A33.
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