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On some infinite integrals involving logarithmic exponential and powers

Published online by Cambridge University Press:  14 November 2011

M. Aslam Chaudhry
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Munir Ahmad
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

Synopsis

In this paper we define an integral function Iμ(α; a, b) for non-negative integral values of μ by

It is proved that the function Iμ(α; a, b) satisfies a functional recurrence-relation which is then exploited to evaluate the infinite integral

Some special cases of the result are also discussed.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1992

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References

1Aslam, M. Chaudhry and Munir Ahmad. On a new probability function with applications (to appear).Google Scholar
2, Erdélyi et al. Higher Transcendental Functions, vol. 1 (New York: McGraw-Hill, 1953).Google Scholar
3, Erdélyi et al. Tables of Integral Transforms, vol. 1 (New York: McGraw-Hill, 1954).Google Scholar
4Budak, B. M. and Fomin, S. V.. Multiple Integrals, Field Theory and Series (Moscow: Mir Publishers, 1978).Google Scholar
5Gradshteyn, I. S. and Ryzhik, I. M.. Tables of Integrals, Series and Products (New York: Academic Press, 1980).Google Scholar
6Ilyin, V. A. and Poznyak, E. G.. Fundamentals of Mathematical Analysis (Moscow: Nauka, 1967).Google Scholar
7Rahman, M.. On a generalization of the Poisson kernel for Jacobi polynomials. SIAM J. Math. Anal. 8(1977), 10141031.CrossRefGoogle Scholar
8Watson, G. N.. A. Treatise on Theory of Bessel Functions (Cambridge: Cambridge University Press, 1966).Google Scholar