J Austral Math Soc Ser B 35 pp469--478, 1994.

On a family of logarithmic and exponential integrals occurring in probability and reliability theory

M. Aslam Chaudhry

(Received 26 May 1992; revised 6 February 1993)

Abstract

We define an integral function I_m(a, x; a, b) for non-negative integral values of m by

I_m(a, x; a, b) = ò_x^¥(ln t) ^m t^{a -

1} exp(-at - bt^-1) dt
(x ³ 0, a > 0, b > 0, -¥ < a < ¥).

It is proved that I_m(a, x; a, b) satisfies a functional recurrence relation which is exploited to find a closed form evaluation of some incomplete integrals. New integral representations of the exponential integral and complimentary error functions are found as special cases.

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Author

M. Aslam Chaudhry: Dept of Math. Sciences, King Fahd Univ. of Petroleum and Minerals, Dhahran, Saudi Arabia.

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