• 호남수학학술지
• /
• 제35권4호
• /
• pp.701-706
• /
• 2013

Summation theorems for hypergeometric series $_2F_1$ and generalized hypergeometric series $_pF_q$ play important roles in themselves and their diverse applications. Some summation theorems for $_2F_1$ and $_pF_q$ have been established in several or many ways. Here we give a proof of Watson's classical summation theorem for the series $_3F_2$(1) by following the same lines used by Rakha [7] except for the last step in which we applied an integral formula introduced by Choi et al. [3].

• 대한수학회논문집
• /
• 제19권4호
• /
• pp.775-778
• /
• 2004

The authors aim at obtaining an interesting result for a special summation formula for $_{6F_5}$(1), by comparing two generalized Watson's theorems on the sum of a $_{3F_2}$ obtained earlier by Mitra and Lavoie et. al.

• Kyungpook Mathematical Journal
• /
• 제47권3호
• /
• pp.449-454
• /
• 2007

InIn this paper we consider generalizations of the classical Dixon's theorem and the classical Whipple's theorem on the sum of a $_3F_2$. The results are derived with the help of generalized Watson's theorem obtained earlier by Mitra. A large number of results contiguous to Dixon's and Whipple's theorems obtained earlier by Lavoie, Grondin and Rathie, and Lavoie, Grondin, Rathie and Arora follow special cases of our main findings.