• 대한수학회논문집
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• 제29권4호
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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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• 제18권2호
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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.

• 호남수학학술지
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• 제38권4호
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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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• 제39권3호
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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.

• 대한수학회논문집
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• 제37권1호
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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.

• 한국안광학회지
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• 제14권3호
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• pp.83-88
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• 2009

목적: 저시력 환자의 경우에 시각적 판단을 위해서 물체의 크기와 노출시간이 상대적으로 커져야 할 필요가 있다고 알려져 왔다. 물체의 크기에 따른 대비감도의 증가를 공간적 가중이라 하며 노출시간에 따른 대비감도의 증가를 시간적 가중이라 하는데 본 연구에서는 저시력 환자들이 시각적 판단 시에 실제로 정상인 보다 큰 물체와 긴 시간을 필요로 하는지 알아보고자 하였다. 방법: 20명의 저시력 환자와 20명의 정상대조군을 대상으로 원형의 사인파격자무늬를 갖는 두 개의 공간주파수 0.7c/d와 3.0c/d로 대비감도를 측정하였다. 자료 분석에는 혼합형 ANOVA(2${\times}$2)를 이용하였다. 결과: 저시력 환자에서의 대비감도는 대조군에 비하여 전반적으로 낮은 값을 보였다. 군간 공간적가중의 변화는 없었으며(p=0.13) 공간주파수간 차는 0.14였으며 이들 간의 상호작용도 유의성이 없었다(p=0.59). 마찬가지로 시간적 가중에서도 군간 시간적 가중의 변화는 통계적 유의성이 없었으며(p=0.19) 공간주파수간 차와 상호작용도 유의성이 없었다(각각 p=0.31, p=0.95). 결론: 정상대조군에 비하여 저시력 군에서 대비감도가 크게 저하되었으나 물체의 크기와 노출시간에 따른 군간 유의한 차이는 없었다.

• 대한수학회논문집
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• 제27권4호
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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.

• 호남수학학술지
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• 제37권2호
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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.

• 대한수학회논문집
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• 제21권3호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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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..