Engineering and physics applications demand a thorough knowledge of applied mathematics and a good understanding of special functions. These functions commonly arise in such areas of applications as heat conduction, communication systems, electro-optics, approximation theory, probability theory, and electric circuit theory, among others. The subject of special functions is quite rich and expanding continuously with the emergence of new problems in the areas of applications in engineering and applied sciences. The solutions of a large body of problems are expressible in terms of some special cases of the most general class of the Meijer G-functions and the Fox .^-functions. The association of hypergeometric functions of several variables and their ^-extensions with the functions arising in theoretical statistics, applied mathematics, and engineering problems seems to be well established. The continuous development in partition theory, combinatorics, astronomy, and others has led to the discovery of new special functions. The development of computational techniques and the advent of computers have increased the importance of the special functions and their formulae. However, it has been noticed that there are several problems in heat conduction and astrophysics where even these most general classes of special functions are not sufficient to accommodate their solutions. We have introduced a class of special functions found useful in the analytic study of several heat conduction problems. Some basic properties of these functions including their recurrence relation, special cases, asymptotic representations, and integral transform relationships are presented.

Chaudhry M.S. Zubair S.M. (2002) On a Class of Incomplete Gamma Functions with Applications.

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