• 충청수학회지
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• 제35권4호
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• pp.277-295
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• 2022

The author proved a modular transformation formula for a function related to generalized non-holomorphic Eisenstein series and, using this formula, established a lot of infinite series identities. In this paper, we find more generalized series relations which contain the author's previous work.

• 한국수학교육학회지시리즈A:수학교육
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• 제51권3호
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• pp.211-221
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• 2012

We discovered that definition of a Geometrical Progression(Sequence) have some differences in domestic textbooks & some foreign countries' books. This will be able to cause a chaos when students divide whether a sequence is a Geometrical Progression(Sequence) or not, and a question error when teachers compose questions about convergence conditions of Infinite Geometric progressions & series. We took a question investigation for students about definition of a Geometrical Progression(that is called G. P.), we discovered that high level students have an error about definition of a G. P.. So We modified expressions of terminology in domestic textbooks appropriately through a Geometrical Progression(Sequence), infinite series, & infinite geometrical series in some foreign countries' books.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권4호
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• pp.233-242
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• 2013

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ${\psi}(z)$, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ${\psi}(z)$. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving $\bar{H}$-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ${\psi}(z)$. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

• Kyungpook Mathematical Journal
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• 제18권2호
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• pp.257-262
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• 1978

In this paper, we obtain two new double infinite series for the H-function of two variables, by which we also obtain a single infinite series involving the H-function of two variable3. On account of the most general nature of the H-functin of two variables, a number of related double infinite series for simpler functions follow as special cases of our results. As an illustration, we obtain here from one of our main series, the corresponding series for $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function and Fox's H-function. A number of other series involving a very large, spectrum of special functions also follow as special cases of our main series but, we are not recording them here for want of space.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제13권2호
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• pp.103-108
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• 2009

We present the thoughts behind a course combining the subjects of differential equations and infinite series. The key point is how to connect the two topics in a course with a natural flow.

• 대한수학회지
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• 제48권1호
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• pp.169-178
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• 2011

In this paper, we find character analogues of infinite series identities which come from a certain modular transformation formula given by B. C. Berndt.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.807-811
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• 2022

In this paper, we have proved a general theorem dealing with φ-| C, α, β |_κ summability factors of infinite series. Also, we have obtained some new and known results related to the different special summability methods.

• 충청수학회지
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• 제22권4호
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• pp.699-716
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• 2009

We deal with a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric $L({\alpha},\;{\beta})$ = ${\beta}{\sum}_{k=0}^{r}(\frac{\alpha}{\beta})^k$ where ${\alpha}<{\beta}$. We introduced a Finsler space $F^n$ with an infinite series $({\alpha},{\beta})$-metric $L({\alpha},\;{\beta})=\frac{\beta^2}{\beta-\alpha}$ and investigated various geometrical properties at [6]. The purpose of the present paper is devoted to finding the condition for a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric above to be a Douglas space.

• 호남수학학술지
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• 제38권3호
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• pp.479-494
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• 2016

In this paper, using a transformation formula for a certain series which comes from the generalized non-analytic Eisenstein series, we obtained some infinite series identities which contain Ramanujan's formula and author's previous results.

• 충청수학회지
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• 제34권2호
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• pp.139-155
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• 2021

Using a modular transformation formula for a class of functions related to generalized non-holomorphic Eisenstein series, we find a new class of infinite series about identities, some of which include generalized formulae of several Berndt's results.