• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.603-607
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• 2005

We give an integral representation for an analogous continued fraction of Ramanujan, for this we first prove an interesting identity.

• The Pure and Applied Mathematics
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• v.8 no.2
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• pp.127-135
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• 2001

The main object of this paper is to present a transformation formula for a finite series involving $_3F_2$ and some identities associated with the binomial coefficients by making use of the theory of Legendre polynomials $P_{n}$(x) and some summation theorems for hypergeometric functions $_pF_q$. Some integral formulas are also considered.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.95-100
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• 2005

In this paper, we consider the finite form of the continued fraction found in the unorganized material, Entry 9 [2], and give the sum of n terms. We give the $n^{th}$ convergent series in two ways-one by simple expansion and the other by using partition theory.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.131-143
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• 2005

We give bibasic expansion for basic Appell functions ${\Phi}^{(1)}$ and ${\Phi}^{(2)}$, and their integral representations. We also give a continued fraction representation for ${\Phi}^{(2)}$.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.169-178
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• 2005

Five results closely related to the well-known Preece's identity obtained earlier by Choi and Rathie will be derived here by using some known hypergeometric identities. In addition to this, the identities obtained earlier by Choi and Rathie have also been written in a compact form.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.509-512
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• 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
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• v.21 no.3
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• pp.569-575
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• 2006

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 $_pF_q$ 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.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.211-220
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• 2005

In this paper we obtain the transformations of the Ramanujan's tenth order mock theta functions under the modular group generators ${\tau}\;{\rightarrow}\;{\tau}\;+\;1\;and\;{\tau}\;{\rightarrow}\;-1/ {\tau}\;where\;q\;=\;e^{{\pi}it}$.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.97-107
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• 2007

Ramanujan gave six identities involving ${\theta}$-function expansion. We extended these identities by introducing a free parameter. We also give the interpretation of one of the identities using theory of partitions.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.249-262
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• 2014

In this paper, we have developed a non-homogeneous q-difference equation of first order for the generalized Mock theta function of order eight and besides these established limiting case of Mock theta functions of order eight. We have also established identities for Partial Mock theta function and Mock theta function of order eight and provided a number of cases of the identities.