Applications to Evaluation of Index Integrals
As it is known from O.I. Marichev (1983), A.P. Prudnikov et al. (1986), (1989a,b), there exists a very important algorithm for evaluation of definite and indefinite integrals of elementary and special functions of hypergeometric type. It covers more than 80 per cent of integrals contained in the world reference literature and also an infinite sets of new integrals. We demonstrated some elements of this algorithm while studying the Mellin convolution type transforms and their representations in the Mellin-Bames type integrals. Almost all of them are reduced to the Mellin convolution (1.98) and then for their evaluations it is appropriate to apply the Mellin transform (1.81) or the Parseval equality (1.99). As for the study of the hypergeometric type of special functions, we can express the value of integral by means of the G- or H-functions, because the integrand of the Mellin-Bames integrals is the gamma-product like (1.47) or (1.51).
KeywordsSpecial Function Type Integral Index Integral Macdonald Function Parseval Equality
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