• 대한수학회논문집
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• 제16권2호
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• pp.319-332
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• 2001

The main object of this paper is first to give tow contiguous analogues of a well-known hypergeometric summation formula for $_2$F$_1$(1/2). We then apply each of these analogues with a view to evaluating the sums of several classes of series in terms of Psi(or Digamma) and the Zeta functions. Relevant connections of the series identities presented here with those given elsewhere are also pointed out.

• Kyungpook Mathematical Journal
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• 제45권2호
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• pp.273-280
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• 2005

We generalize a continued fraction of Ramanujan by introducing a free parameter. We give the closed form for the continued fraction. We also consider the finite form giving $n^{th}$ convergent using partition theory.

• 대한수학회논문집
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• 제12권4호
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• pp.1065-1067
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• 1997

The aim of this research is to derive an interesting formula due to Bailey by a very short method.

• Kyungpook Mathematical Journal
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• 제32권2호
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• pp.153-158
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• 1992

• East Asian mathematical journal
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• 제14권1호
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• pp.157-163
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• 1998

The aim of this note is to prove Vandermonde's convolution theorem by using the theory of hypergeometric series as suggested in literature which does not seem to be easy to justify it. We also provide an interesting identity and its application.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.341-345
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• 2007

In this paper we show that the second order mock theta function, given by Hikami, is bounded and satisfies the second condition for the mock theta functions.

• East Asian mathematical journal
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• 제15권1호
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• pp.29-38
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• 1999

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.603-607
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• 2005

We give an integral representation for an analogous continued fraction of Ramanujan, for this we first prove an interesting identity.

• 대한수학회보
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• 제57권2호
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• pp.345-354
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• 2020

In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of ₂𝜓₂ series $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a,c;q)_n}{(b,d;q)_n}}z^n$$ and Ramanujan's sum $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a;q)_n}{(b;q)_n}}z^n$$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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• pp.87-102
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• 2012

In this paper, we consider the Fourier-type functionals introduced in [16]. We then establish the analytic Feynman integral for the Fourier-type functionals. Further, we get a series expansion of the analytic Feynman integral for the Fourier-type functional $[{\Delta}^kF]^{\^}$. We conclude by applying our series expansion to several interesting functionals.