Barton Willis wrote:
> My Maple tells me that integrate(hypergeometric([1],[2],z),z) = z *
> hypergeometric([1, 1],[2, 2],z),
> but I don't know the general rule. Can we do better than an error?
>
None of the references at hand had it, but fortunately I could view the
relevant page of
Prudnikov at amazon.com. We need 1.16.1.2 for the case when one of the
a_i equals 1.
;; Integrals and Series: Volume 3, More Special Functions
;; Prudnikov, A. P., Brychkov, Yu A., Gould, G. G., Marichev, O.I.
;;
;; /
;; [
;; I pFq((a_p);(b_q);c z) dz
;; ]
;; /
;;
;; = z (p+1)F(q+1)((a_p),1;(b_q),2;c z) 1.16.1.2
;;
;; product((b_q - 1))
;; = ------------------ pFq((a_p)-1; (b_q)-1; c z) 1.16.1.3
;; product((a_p - 1))
I have checked in a fix.