The Calculation and Application of the Partial Derivatives of the Generalized Hypergeometric Function.

In this paper, a algorithm of the partial derivatives of the generalized hypergeometric function pFq ( ã; ˜b; z ) is obtained, where ã = {a1, a2, . . ., ap}, ˜b = {b1, b2, . . ., bq}. Moreover, we compare some algorithms of calculating the partial derivatives of pFq ( ã; ˜b; z ) . Numerical examples show the algorithm given in this paper improves the precision and accelerates the calculation of partial derivatives of the generalized hypergeometric function. Furthermore, we obtain some applications of the partial derivatives of the generalized hypergeometric function in calculating improper integrals and the derivative of the special function, such as the derivatives with respect to the order of Bessel function etc. The accuracy and the speed of calculating the improper integrals are improved by numerical examples. [ABSTRACT FROM AUTHOR]