• Honam Mathematical Journal
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• v.34 no.1
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• pp.35-44
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• 2012

Motivated by the extension of classical Dixon's summation theorem for the series $_3F_2$ given by Lavoie, Grondin, Rathie and Arora, the authors aim at deriving four generalized summation formulas, which, upon specializing their parameters, give many summation identities including, especially, the four very interesting summation formulas due to Ramanujan.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.367-377
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• 2022

Let G be a non-discrete locally compact abelian group, and 𝜇 be a transformable and translation bounded Radon measure on G. In this paper, we construct a Segal algebra S_𝜇(G) in L¹(G) such that the generalized Poisson summation formula for 𝜇 holds for all f ∈ S_𝜇(G), for all x ∈ G. For the definitions of transformable and translation bounded Radon measures and the generalized Poisson summation formula, we refer to L. Argabright and J. Gil de Lamadrid's monograph in 1974.

• 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.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.701-706
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• 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].

• East Asian mathematical journal
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• v.33 no.5
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• pp.527-531
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• 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 $_pF_q$.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.527-534
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• 2013

We first aim at proving an interesting easily derivable summation formula. Then it is easily seen that this formula immediately yields a hypergeometric summation theorem recently added to the literature by Qureshi et al. Moreover we apply the main formulas to present some interesting summation formulas, whose special cases are also seen to yield the earlier known results.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.775-778
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• 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
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• v.30 no.3
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• pp.227-237
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• 2015

By employing certain extended classical summation theorems, several surprising ${\pi}$ and other formulae are displayed.

• Communications of the Korean Mathematical Society
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• v.30 no.2
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• pp.103-108
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• 2015

Fox [2] presented an interesting identity for $_pF_q$ which is expressed in terms of a finite summation of $_pF_q$'s whose involved numerator and denominator parameters are different from those in the starting one. Moreover Fox [2] found a very interesting and general summation formula for $_3F_2(1/2)$ as a special case of his above-mentioned general identity with the help of Kummer's second summation theorem for $_2F_1(1/2)$. Here, in this paper, we show how two general summation formulas for $$_3F_2\[\array{\hspace{110}{\alpha},{\beta},{\gamma};\\{\alpha}-m,\;\frac{1}{2}({\beta}+{\gamma}+i+1);}\;{\frac{1}{2}}\]$$, m being a nonnegative integer and i any integer, can be easily established by suitably specializing the above-mentioned Fox's general identity with, here, the aid of generalizations of Kummer's second summation theorem for $_2F_1(1/2)$ obtained recently by Rakha and Rathie [7]. Several known results are also seen to be certain special cases of our main identities.

• 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.