• East Asian mathematical journal
• /
• v.18 no.1
• /
• pp.111-125
• /
• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• Communications of the Korean Mathematical Society
• /
• v.22 no.4
• /
• pp.509-512
• /
• 2007

We aim at deriving Gauss's second summation theorem for the series $_2F_1(1/2)$ by using Euler's integral representation for $_2F_1$. It seems that this method of proof has not been tried.

• Communications of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.835-850
• /
• 2017

A remarkably large number of special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) have been investigated by many authors. Motivated the works of both works of both Burchnall and Chaundy and Chaundy and very recently, Brychkov and Saad gave interesting generalizations of Appell type functions. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present some new differential formulas for the generalized Appell's type functions ${\kappa}_i$, $i=1,2,{\ldots},18$ by considering the product of two $_4F_3$ functions.

• Communications of the Korean Mathematical Society
• /
• v.15 no.1
• /
• pp.71-75
• /
• 2000

The object of this note is to introduce three Ramanuian's formulae of similar nature among his many curious ones and to prove them by making use of the theory of generalized hypergeometric series.

• East Asian mathematical journal
• /
• v.15 no.2
• /
• pp.201-210
• /
• 1999

Morley provided an interesting identity about 20 years earlier before its more generalized form was given by Dixon. In this note some of its generalized forms and an application of Morley's formula are considered.

• Communications of the Korean Mathematical Society
• /
• v.19 no.4
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.15 no.1
• /
• pp.51-57
• /
• 2000

The aim of this research is to provide twenty five integrals involving hypergeometric function in the form of a single integral. Fifty two interesting integrals follow as special cases of our main findings. These results are obtained with the help of generalized Watson's theorem on the sum of a $_3$F$_2$ recently obtained by Lavoie, Grondin and Rathie. The integrals given in this paper are simple, interesting and easily established, and they may be useful.

• Honam Mathematical Journal
• /
• v.34 no.4
• /
• pp.603-614
• /
• 2012

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. In this sequel, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in $m$ variables to present two generating functions of the generalized Gottlieb polynomials ${\varphi}^m_n({\cdot})$. Here, we show that many formulas regarding the Gottlieb polynomials in m variables and their reducible cases can easily be obtained by using one of two generating functions for Choi's generalization of the Gottlieb polynomials in m variables expressed in terms of well-developed Lauricella series $F^{(m)}_D[{\cdot}]$.

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.135-146
• /
• 2001

Several families of infinite series were summed recently by means of certain operators of fractional calculus(that is, calculus of derivatives and integrals of any real or complex order). In the present sequel to this recent work, it is shown that much more general classes of infinite sums can be evaluated without using fractional calculus. Some other related results are also considered.

• East Asian mathematical journal
• /
• v.33 no.5
• /
• pp.527-531
• /
• 2017

We aim to prove a known summation formula for the series $_4F_3(1)$ by mainly using a similar method as in [2], which is different from that in [3]. The method of proof here as well as that in [2] is potentially useful in getting some other summation formulas for $_pF_q$.