Parameter derivatives of the generalized hypergeometric function
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Answer:
Step-by-step explanation:
The first derivatives for some special values of the parameters were already known long time ago [12] [14]. Later on, Ancarani et al. have found in a series of papers [4], [5] and [8] the derivatives of Gaussian hypergeometric functions, and some derivatives of two-variable series, namely the Appell series and four degenerate confluent series [6]. Moreover, it has been shown, that the first derivatives of generalized hypergeometric functions is expressible in the terms of Kampé de Fériet functions and, with the same technique, derivatives of the Appell hypergeometric function was obtained in paper [7]. ...
... As a first step we consider the derivative of a hypergeometric function in the parameter a in the case when the Pochhammer symbol contains only one index of summation, (a) n. As mentioned above, our calculations in this Section are similar to the [1] [8]. The main trick is to consider the derivative of the Pochhammer symbol (a) n. ...