Generalizations of Gauss's second summation theorem and Bailey's formula for the series $_2 F_1 (1/2)$

摘要

We aim mainly at presenting two generalizations of the well-known Gauss's second summation theorem and Bailey's formula for the series $_2F_1 (1/2)$. An interesting transformation formula for $_p F_q$ is obtained by combining our two main results. Relevant connections of some special cases of our main results with those given here or elsewhere are also pointed out.