EXTENSION OF GANELIUS' THEOREM

Park, Ae-Young; Park, Ae-Young

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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ISSN : 1226-0657

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Vol.3 No.1

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

1996, v.3 no.1, pp.95-101

Park, Ae-Young

Park,, A. (1996). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 3(1), 95-101.

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Abstract

In this paper, we extend Ganelius' lemma in Anderson [1]. In the Ganelius' original version several of the <TEX>${\alpha}$</TEX><TEX>$\sub$</TEX>k/ are equal to 1, but in our extension theorem we have the <TEX>${\alpha}$</TEX><TEX>$\sub$</TEX>k/ distinct and all unequal to 1. Then our theorem can be used to introduce an indefinite quadrature formula for ∫<TEX>$\sub$</TEX>-1/<TEX>$\^$</TEX>1/ f(<TEX>$\chi$</TEX>)d<TEX>$\chi$</TEX>, f <TEX>$\in$</TEX> H<TEX>$\^$</TEX>p/, with p ＞ 1. We will also correct an error in the proof of Ganelius' theorem provided in Ganelius [2].(omitted)

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Article Contents

Vol.3 No.1

Abstract

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics