• 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.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.661-666
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• 2019

In this short research note, we aim to provide a new proof of classical Dixon's summation theorem for the series $_3F_2$ with unit argument. The theorem is obtained by evaluating an infinite integral and making use of classical Gauss's and Kummer's summation theorem for the series $_2F_1$.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.467-472
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• 2012

The aim of this paper is to provide two interesting summation formulae with the argument unity for the generalized hypergeometric function of higher order. The results are obtained with the help of two new summation formulae very recently obtained by Kim et al.. Summation formulae obtained earlier by Carlson and re-derived by Exton turn out to be special cases of our main findings.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.25-37
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• 2016

In 1972, Andrews derived the basic analogue of Gauss's second summation theorem and Bailey's theorem by implementing basic analogue of Kummer's theorem into identity due to Jackson. Recently Lavoie et.al. derived many results closely related to Kummer's theorem, Gauss's second summation theorem and Bailey's theorem and also Rakha et. al. derive the basic analogues of results closely related Kummer's theorem. The aim of this paper is to derive basic analogues of results closely related Gauss's second summation theorem and Bailey's theorem. Some applications and limiting cases are also considered.

• 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].

• Honam Mathematical Journal
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• v.35 no.1
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• pp.83-92
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• 2013

The aim of this research paper is to provide certain generalizations of two well-known summations due to Ramanujan. The results are derived with the help of the generalized Dixon's theorem on the sum of $_3F_2$ and the generalized Kummer's theorem for $_2F_1$ obtained earlier by Lavoie et al. [3, 5]. As their special cases, we have obtained fifteen interesting summations which are closely related to Ramanujan's summation.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.223-228
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• 2005

In 2001, Choi, Harsh & Rathie [Some summation formulas for the Appell's function $F_1$. East Asian Math. J. 17 (2001), 233-237] have obtained 11 results for the Appell's function $F_1$ with the help of Gauss's summation theorem and generalized Kummer's summation theorem. We aim at presenting 22 more results for $F_1$ with the help of the generalized Gauss's second summation theorem and generalized Bailey's theorem obtained by Lavoie, Grondin & Rathie [Generalizations of Whipple's theorem on the sum of a $_3F_2$. J. Comput. Appl. Math. 72 (1996), 293-300]. Two interesting (presumably) new special cases of our results for $F_1$ are also explicitly pointed out.

• 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.

• The Korean Journal of Pain
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• v.14 no.1
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• pp.19-25
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• 2001

Background: Transcutaneous electrical nerve stimulation (TENS) has been used widely, but its effects are controversial. This is probably due to the varying intensity and type of pain. We designed a study to assess the effects of the TENS on the RIII nociceptive flexion reflex as the resting pain level and the temporal summation as a repeated, movement related pain in 7 normal volunteer subjects. Methods: High frequency (80 Hz), non-noxious TENS was applied over the left popliteal fossa for 20 minutes. Ipsilateral RIII reflexes induced by single electrical stimulus and temporal summation of pain responses to repeated stimuli (five stimuli at 2 Hz) were recorded before, during (just before stopping), and subsequently at 20 minutes after TENS. Results: R (III) nociceptive flexion reflex activity during and after TENS was more significantly decreased than before treatment. However, the temporal summation threshold was not changed. Conclusions: We conclude that high frequency, non-noxious TENS could be effective on resting pain relief in the same segment but not on the movement related pain.

• Kyungpook Mathematical Journal
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• v.18 no.2
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• pp.217-221
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• 1978

In this paper we prove three summation formulae for hypergeometric series $_2F_1({\frac{1}{2}})$.