翻訳と辞書 Words near each other ・ Lidor Cohen ・ Lidor Cohen (footballer born 1992) ・ Lidor Yosefi ・ Lidoriki ・ Lidoro Oliver ・ Lidov ・ Lidovka ・ Lidové noviny ・ Lidrezing ・ LIDS ・ Lids (store) ・ Lidsing ・ Lidster ・ Lidstone ・ Lidstone (surname) ・ Lidstone series ・ Lidströmer ・ Lidsville ・ Lidth's jay ・ Lidtke Mill ・ Lidu Yangtze River Bridge ・ Lidui Park Railway Station ・ Lidung Jelo ・ Lidushik ・ Lidwina ・ Lidy Creek ・ Lidy Prati ・ Lidy Stoppelman ・ Lidy Walker Covered Bridge ・ Lidya Tchakerian Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lidstone series ： ウィキペディア英語版 Lidstone series In mathematics, a Lidstone series, named after George James Lidstone, is a kind of polynomial expansion that can expressed certain types of entire functions. Let ''ƒ''(''z'') be an entire function of exponential type less than (''N'' + 1)''π'', as defined below. Then ''ƒ''(''z'') can be expanded in terms of polynomials ''A''''n'' as follows: :$f(z)=\backslash sum\_^\backslash infty\; \backslash left(A\_n(1-z)\; f^(0)\; +\; A\_n(z)\; f^(1)\; \backslash right)\; +\; \backslash sum\_^N\; C\_k\; \backslash sin\; (k\backslash pi\; z).$ Here ''A''''n''(''z'') is a polynomial in ''z'' of degree ''n'', ''C''''k'' a constant, and ''ƒ''(''n'')(''a'') the ''n''th derivative of ''ƒ'' at ''a''. A function is said to be of exponential type of less than ''t'' if the function :$h(\backslash theta;\; f)\; =\; \backslash underset\backslash ,\; \backslash frac\; \backslash log\; |f(r\; e^)|\backslash ,$ is bounded above by ''t''. Thus, the constant ''N'' used in the summation above is given by :$t=\; \backslash sup\_\; h(\backslash theta;\; f)\backslash ,$ with : ==References== * Ralph P. Boas, Jr. and C. Creighton Buck, ''Polynomial Expansions of Analytic Functions'', (1964) Academic Press, NY. Library of Congress Catalog 63-23263. Issued as volume 19 of ''Moderne Funktionentheorie'' ed. L.V. Ahlfors, series ''Ergebnisse der Mathematik und ihrer Grenzgebiete'', Springer-Verlag ISBN 3-540-03123-5 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lidstone series」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.