• East Asian mathematical journal
• /
• v.14 no.2
• /
• pp.321-327
• /
• 1998

There have been various proofs of the Legendre duplication formula for the Gamma function. Another proof of the formula is given here and a brief history of the Gamma function is also provided.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.289-294
• /
• 1996

The double Gamma function had been defined and studied by Barnes [4], [5], [6] and others in about 1900, not appearing in the tables of the most well-known special functions, cited in the exercise by Whittaker and Waston [25, pp. 264]. Recently this function has been revived according to the study of determinants of Laplacians [8], [11], [15], [16], [19], [20], [22] and [24]. Shintani [21] also uses this function to prove the classical Kronecker limit formula. Its p-adic analytic extension appeared in a formula of Casson Nogues [7] for the p-adic L-functions at the point 0.

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.129-133
• /
• 2001

The aim of this research note is to derive the well known Kummer's second theorem by transforming the integrals which represent some generalized hypergeometric functions. This theorem can also be shown by combining two known Bailey's and Preece's identities for the product of generalized hypergeometric series.

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.147-158
• /
• 2001

The Gauss summation theorem plays a key role in the theory of(generalized) hypergeometric series. The authors study several proofs of the theorem and consider some applications of it.

• Honam Mathematical Journal
• /
• v.35 no.4
• /
• 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].