• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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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.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.603-608
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• 2005

In 1999 and 2003, Padmanabham established two results (one each) for Exton's triple hypergeometric series $X_8$. We aim at showing that Exton's later result can be derived from his former one.

• East Asian mathematical journal
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• v.17 no.2
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• pp.197-215
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• 2001

A generalised Taylor series with integral remainder involving a convex combination of the end points of the interval under consideration is investigated. Perturbed generalised Taylor series are bounded in terms of Lebesgue p-norms on $[a,b]^2$ for $f_{\Delta}:[a,b]^2{\rightarrow}\mathbb{R}$ with $f_{\Delta}(t,s)=f(t)-f(s)$.

• Korean Journal of Pharmacognosy
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• v.51 no.4
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• pp.278-290
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• 2020

The purpose of this study is to investigate the hangover relieving effect of HO-series. HO-S1 is an herbal mixture, which consists of extracts from Flower of Pueraria lobata Ohwi, Glycyrrhiza glabra Linné, Fruit of Lycium chinense Miller, Poria cocos Wolf, Acanthopanax sessiliflorum Seeman, Scutellaria baicalensis Georgi, Atractylodes lancea De Candlle and Zingiber officinale Roscoe. HO-S2 is a candidate that has been performed to ultra filtration based on HO-S1. HO-S3 is a mixture of amino acids and vitamins based on HO-S2. HO-01 is the final beverage base produced based on HO-S3. The antioxidant activity of HO-series was similar to that of vitamin C or trolox. The production of t-BHP induced reactive oxygen species(ROS) was significantly blocked in the presence of HO-series. In vivo study, AUC of alcohol and acetaldehyde concentrations in HO-S2 and HO-S3 treated groups significantly decreased. Hepatic alcohol dehydrogenase(ADH) and acetaldehyde dehydrogenase(ALDH) activity were significantly higher in HO-S2 and HO-S3 treated groups. And 2E1 activity and glutathione were significantly elevated, while the malondialdehyde level was not significantly in liver tissue. After alcohol exposure, the sensitivity scores of blood alcohol and acetaldehyde concentration and hangover symptoms were significantly decreased in the HO-01 intake group compared with the non-intake group. ALDH activity was significantly increased in the HO-01 intake group. HO-series have antioxidant activity and a protective effect from ROS. HO-S2, HO-S3 and HO-01 are potentially highly beneficial in relieving hangover, as it scavenges reactive free radicals and boosts the endogenous antioxidant system.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.435-450
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• 2024

This study depends on the modified conformable fractional derivative definition to generalize and proves some theorems of the classical power series into the fractional power series. Furthermore, a comprehensive formulation of the generalized Taylor's series is derived within this context. As a result, a new technique is introduced for the fractional power series. The efficacy of this new technique has been substantiated in solving some fractional differential equations.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.299-312
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• 2012

In 1970s, B. C. Berndt proved a transformation formula for a large class of functions that includes the classical Dedekind eta function. From this formula, he evaluated several classes of infinite series and found a lot of interesting infinite series identities. In this paper, using his formula, we find new infinite series identities.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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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.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.407-415
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• 2013

Very recently, Rakha and Rathie obtained an extension of the classical Saalsch$\ddot{u}$tz's summation theorem. Here, in this paper, we first give an elementary proof of the extended Saalsch$\ddot{u}$tz's summation theorem. By employing it, we next present certain extenstions of Ramanujan's result and another result involving hypergeometric series. The results presented in this paper are simple, interesting and (potentially) useful.

• 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].