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Titlebook: Ramanujan‘s Lost Notebook; Part II George E. Andrews,Bruce C. Berndt Book 2009 Springer-Verlag New York 2009 Invariant.approximation.ellipt

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书目名称Ramanujan‘s Lost Notebook
副标题Part II
编辑George E. Andrews,Bruce C. Berndt
视频video
概述Most of this material has never before been published in book form.Authors have organized, and provided commentary on, Ramanujan‘s results.Discusses q-series, Eisenstein series, and theta functions.In
图书封面Titlebook: Ramanujan‘s Lost Notebook; Part II George E. Andrews,Bruce C. Berndt Book 2009 Springer-Verlag New York 2009 Invariant.approximation.ellipt
描述This is the second of approximately four volumes that the authors plan to write in their examination of all the claims made by S. Ramanujan in The Lost Notebook and Other Unpublished Papers. This volume, published by Narosa in 1988, contains the “Lost Notebook,” which was discovered by the ?rst author in the spring of 1976 at the library of Trinity College, Cambridge. Also included in this publication are other partial manuscripts, fragments, and letters that Ramanujan wrote to G. H. Hardy from nursing homes during 1917–1919. The authors have attempted to organize this disparate material in chapters. This second volume contains 16 chapters comprising 314 entries, including some duplications and examples, with chapter totals ranging from a high of ?fty-four entries in Chapter 1 to a low of two entries in Chapter 12. Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Introduction . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 The Heine Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 1 Introduction . . . . . .
出版日期Book 2009
关键词Invariant; approximation; elliptic function; equation; function; identity; theta function; transformation
版次1
doihttps://doi.org/10.1007/b13290
isbn_softcover978-1-4419-2666-1
isbn_ebook978-0-387-77766-5
copyrightSpringer-Verlag New York 2009
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The Heine Transformation,E. Heine [178], [179, pp. 97–125] was the first to generalize Gauss’s hypergeometric series to .-hypergeometric series by defining, for ., ., where . and where, for each nonnegative integer ., ..
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Well-Poised Series,Among Ramanujan’s most far-reaching and striking discoveries are the Rogers–Ramanujan identities, given for . by [241], [31, Chapter 10] . and . In the lost notebook, we find many identities of the Rogers–Ramanujan type; see, for example, Chapter 11 of our first book [31].
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,Bailey’s Lemma and Theta Expansions,Most of the entries to be established in this chapter were originally proved in [22]. That paper appeared before the discoveries presented in [24] were made. It is now possible to present these results in a way that makes clear their relationship to the hierarchy of .-hypergeometric identities growing out of Bailey’s lemma [41, equation (3.1)].
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Two Letters on Eisenstein Series Written from Matlock House,As we mentioned in Chapter 11, in their last joint paper, G.H. Hardy and Ramanujan [177], [242, pp. 310–321] established the following remarkable formula for the coefficients of 1/...Then,
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