• Journal of the Korean Statistical Society
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• 제29권3호
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• pp.315-318
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• 2000

In this note we use the Poisson Summation Formula to generalize a result of Harris and Park (1994) on lattice distributions induced by uniform (0,1) random variables to those generated by random variables with step functions as their probability functions.

• East Asian mathematical journal
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• 제22권1호
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• pp.71-77
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• 2006

By applying various known summation theorems to a general transformation formula based upon Bailey's transformation theorem due to Slater, Exton has obtained numerous and new quadratic transformations involving hypergeometric functions of order greater than two(some of which have typographical errors). We aim at first deriving a general quadratic transformation formula due to Exton and next providing a list of quadratic formulas(including the corrected forms of Exton's results) and some more results.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.731-742
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• 2009

In this paper, by introducing parameters ${\lambda}$, ${\alpha}$and two pairs of conjugate exponents (p, q), (r, s) and applying the improved Euler-Maclaurin's summation formula, we establish a reverse of the slightly sharper Hilbert-type inequality. As applications, the strengthened version and the equivalent form are given.

• Journal of the Korean Statistical Society
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• 제32권1호
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• pp.21-24
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• 2003

In the recent papers by Harris and Park (1994) and by Hui and Park (2000), a family of lattice distributions derived from a sum of independent identically distributed random variables is examined. In this paper we generalize a result of Hui and Park (2000) on lattice distributions on the torus using the Poisson summation formula.

• East Asian mathematical journal
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• 제25권4호
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• pp.481-486
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• 2009

The first object of this note is to show that a summation formula due to Padmanabham for three-variables hypergeometric function $X_8$ introduced by Exton can be proved in a different (from Padmanabham's and his observation) yet, in a sense, conventional method, which has been employed in obtaining a variety of identities associated with hypergeometric series. The second purpose is to point out that one of two seemingly new hypergeometric identities due to Exton was already recorded and the other one is easily derivable from the first one. A corrected and a little more compact form of a general transform involving hypergeometric functions due to Exton is also given.

• East Asian mathematical journal
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• 제17권1호
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• pp.147-158
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• 2001

The Gauss summation theorem plays a key role in the theory of(generalized) hypergeometric series. The authors study several proofs of the theorem and consider some applications of it.

• 호남수학학술지
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• 제34권3호
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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.

• 호남수학학술지
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• 제35권1호
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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.

• 대한수학회논문집
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• 제9권4호
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• pp.853-855
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• 1994

The object of present note is to give a very short proof of Stirling's formula which uses only a formula for the generalized zeta function. There are several proofs for this formula. For example, Dr. E. J. Routh gave an elementary proof using Wallis' theorem in lectures at Cambridge ([5, pp.66-68]). We can find another proof which used the Maclaurin summation formula ([5, pp.116-120]). In [1], they used the Central Limit Theorem or the inversion theorem for characteristic functions. In [2], pp. Diaconis and D. Freeman provided another proof similarly as in [1]. J. M. Patin [7] used the Lebesgue dominated convergence theorem.

• Kyungpook Mathematical Journal
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• 제13권2호
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• pp.249-251
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• 1973