Closed-form evaluation of integrals involving the gamma function

In this article, we obtain simplified as well as original closed-form expressions for integrals involving the gamma function. These explicit results are found neither in the literature nor using symbolic computation software. Subsequent results follow, giving rise to explicit expressions for integrals involving the error function, with application in order statistics. In particular, these results can be used within the framework of reliability theory.     

HITTING LINES and CIRCLES WITH DIFFUSION PROCESSES

For (x(t),y(t)), a diffusion process starting from (x(0),y(0)) = (x,y), the problem of computing the moment generating function of the first passage time T(x, y) to a given subset D of IR²is considered. A particular case of the method of similarity solutions is used. The problems that can be solved explicitly are those for which D is either a straight line or a circle.