Certain decomposition formulas of generalized hypergeometric functions ${}_pF_q$ and some formulas of an analytic continuation of the Clausen function ${}_3F_2$

摘要

Here, by using the symbolical method introduced by Burchnall and Chaundy, we aim at constructing certain expansion formulas for the generalized hypergeometric function ${}_pF_q$. In addition, using our expansion formulas for ${}_pF_q$, we present formulas of an analytic continuation of the Clausen hypergeometric function ${}_3F_2$, which are much simpler than an earlier known result. We also give some integral representations for ${}_3F_2$.