• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.519-526
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• 2014

A large number of summation and transformation formulas involving (generalized) hypergeometric functions have been developed by many authors. Here we aim at establishing two (presumably) new general hypergeometric transformations. The results are derived by manipulating the involved series in an elementary way with the aid of certain hypergeometric summation theorems obtained earlier by Rakha and Rathie. Relevant connections of certain special cases of our main results with several known identities are also pointed out.

• Kyungpook Mathematical Journal
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• v.18 no.2
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• pp.211-215
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• 1978

In the present paper, we obtain two new and interesting finite summation formulae for the H-function of two variables in a very neat and elegant form. The novel feature of the paper is that the method used here in deriving these formulae is simple and direct and does not impose heavy restrictions on the parameters involved. On account of the most general nature of the H-function of two variables, a number of related finite summation formulae for a number of other useful functions can also be obtained as special cases of our results. As an illustration, we have obtained here from our main results, the corresponding finite summation formulae for $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function. Appell's function and Gauss' hypergeometric function which are also believed to be new.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.849-856
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• 2016

General summation formula for sums involving ${\sigma}(n)/n$ is expressed with infinite series containing a Bessel function.

• East Asian mathematical journal
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• v.39 no.3
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• pp.299-303
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• 2023

The aim of this note is to provide three derivations of the well-known Gregory-Leibniz series for π via a hypergeometric series approach.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.293-301
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• 2022

The present paper concerns with a study of certain generating functions and summation formulas of generalized Poisson-Charlier polynomials. Some special cases are also discussed.

• Journal of Korean Ophthalmic Optics Society
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• v.14 no.3
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• pp.83-88
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• 2009

Purpose: It is said that persons with low vision (LV) require larger object and longer exposure time to make a visual judgment. The spatial summation stands for the increasing of contrast sensitivity (CS), as the target size is enlarged. Likewise, the term temporal summation is used when the CS increases as the exposure duration is extended. The present study investigates whether or not greater target and longer exposure duration is required for LV subjects than for control subjects. Methods: Twenty subjects with LV and twenty age-matched controls took part in the study. The CS was measured with a 2 alternative forced choice stair case for 0.7 and 3.0 cycle per degree (c/d) static sinusoidal gratings within a circular aperture. The results were analyzed by mixed ANOVA (2${\times}$2). Results: As expected, the CS in the LV group were overall depressed. For spatial summation, mixed ANOVA (2 groups${\times}$2 spatial frequencies) gave p values of 0.13 for the effect of group, 0.14 for spatial frequency and there was no interaction (p=0.59). Similarly, for temporal summation the results were p=0.19 for group, 0.31 for spatial frequency and p=0.95 for interaction. Conclusions: Despite the depression of CS in the LV group, a significant difference for spatial and temporal summation between two subject groups was not reached.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.745-751
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• 2012

The aim of this research note is to provide the sums of the series $$\sum_{k=0}^{\infty}(-1)^k\({{a-i}\atop{k}}\)\frac{1}{2^k(a+k+1)}$$ for $i$ = 0, ${\pm}1$,${\pm}2$,${\pm}3$,${\pm}4$,${\pm}5$. The results are obtained with the help of generalization of Bailey's summation theorem on the sum of a $_2F_1$ obtained earlier by Lavoie et al.. Several interesting results including those obtained earlier by Srivastava, Vowe and Seiffert, follow special cases of our main findings. The results derived in this research note are simple, interesting, easily established and (potentially) useful.

• Honam Mathematical Journal
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• v.37 no.2
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• pp.245-252
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• 2015

This paper is in continuation of the paper very recently published [New Laplace transforms of Kummer's confluent hypergeometric functions, Math. Comp. Modelling, 55 (2012), 1068-1071]. In this paper, our main objective is to show one can obtain so far unknown Laplace transforms of three rather general cases of generalized hypergeometric function $_2F_2(x)$ by employing generalized Watson's, Dixon's and Whipple's summation theorems for the series $_3F_2$ obtained earlier in a series of three research papers by Lavoie et al. [5, 6, 7]. The results established in this paper may be useful in theoretical physics, engineering and mathematics.

• 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.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.255-259
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• 2006

In 1994, Lavoie et al. have obtained twenty tree interesting results closely related to the classical Dixon's theorem on the sum of a $_3F_2$ by making a systematic use of some known relations among contiguous functions. We aim at showing that these results can be derived by using the same technique developed by Bailey with the help of Gauss's summation theorem and generalized Kummer's theorem obtained by Lavoie et al..