標(biāo)題: Titlebook: Ramanujan‘s Lost Notebook; Part II George E. Andrews,Bruce C. Berndt Book 2009 Springer-Verlag New York 2009 Invariant.approximation.ellipt [打印本頁] 作者: 不同 時間: 2025-3-21 18:12
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書目名稱Ramanujan‘s Lost Notebook讀者反饋學(xué)科排名
作者: 量被毀壞 時間: 2025-3-21 22:19 作者: 搏斗 時間: 2025-3-22 04:13
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 ., ..作者: Anecdote 時間: 2025-3-22 05:26 作者: 摻和 時間: 2025-3-22 10:01 作者: 初次登臺 時間: 2025-3-22 16:16
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].作者: Protein 時間: 2025-3-22 19:52
,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)].作者: Folklore 時間: 2025-3-23 01:08 作者: 自負(fù)的人 時間: 2025-3-23 04:55
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,作者: Trigger-Point 時間: 2025-3-23 05:38 作者: adulterant 時間: 2025-3-23 09:43 作者: Blood-Vessels 時間: 2025-3-23 17:39 作者: Phenothiazines 時間: 2025-3-23 20:45
978-1-4419-2666-1Springer-Verlag New York 2009作者: BRINK 時間: 2025-3-24 00:00 作者: 盡忠 時間: 2025-3-24 02:33 作者: 包裹 時間: 2025-3-24 09:05 作者: KIN 時間: 2025-3-24 11:47 作者: 煞費苦心 時間: 2025-3-24 17:34 作者: 王得到 時間: 2025-3-24 22:32
Bruce C. Berndt,George E. Andrewsart III has also been expanded through the addition of four new appendices. From "asset pricing models" to "risk management," the Encyclopedia of Finance, Second Edition, serves as an essential resource for academics, educators, and students.978-1-4614-5360-4作者: engrossed 時間: 2025-3-25 02:12 作者: 過度 時間: 2025-3-25 05:03
Bruce C. Berndt,George E. Andrewsart III has also been expanded through the addition of four new appendices. From "asset pricing models" to "risk management," the Encyclopedia of Finance, Second Edition, serves as an essential resource for academics, educators, and students.978-1-4614-5360-4作者: 阻礙 時間: 2025-3-25 09:12 作者: 高深莫測 時間: 2025-3-25 12:08 作者: DNR215 時間: 2025-3-25 16:18 作者: 狂亂 時間: 2025-3-25 23:42 作者: ZEST 時間: 2025-3-26 03:40
Bruce C. Berndt,George E. Andrewsart III has also been expanded through the addition of four new appendices. From "asset pricing models" to "risk management," the Encyclopedia of Finance, Second Edition, serves as an essential resource for academics, educators, and students.978-1-4614-5360-4作者: 五行打油詩 時間: 2025-3-26 06:57 作者: 我不怕犧牲 時間: 2025-3-26 10:54
Bruce C. Berndt,George E. Andrewsart III has also been expanded through the addition of four new appendices. From "asset pricing models" to "risk management," the Encyclopedia of Finance, Second Edition, serves as an essential resource for academics, educators, and students.978-1-4614-5360-4作者: Irrigate 時間: 2025-3-26 13:14
Bruce C. Berndt,George E. Andrewsart III has also been expanded through the addition of four new appendices. From "asset pricing models" to "risk management," the Encyclopedia of Finance, Second Edition, serves as an essential resource for academics, educators, and students.978-1-4614-5360-4作者: 枯萎將要 時間: 2025-3-26 17:35
Bruce C. Berndt,George E. Andrewsart III has also been expanded through the addition of four new appendices. From "asset pricing models" to "risk management," the Encyclopedia of Finance, Second Edition, serves as an essential resource for academics, educators, and students.978-1-4614-5360-4作者: 琺瑯 時間: 2025-3-27 00:23 作者: 公豬 時間: 2025-3-27 02:55 作者: CLAY 時間: 2025-3-27 09:13
Bruce C. Berndt,George E. Andrewsart III has also been expanded through the addition of four new appendices. From "asset pricing models" to "risk management," the Encyclopedia of Finance, Second Edition, serves as an essential resource for academics, educators, and students.978-1-4614-5360-4作者: 輕推 時間: 2025-3-27 10:45
Bruce C. Berndt,George E. Andrewstates for the past three decades. In the winter 2005 issue of the Journal of Finance Literature, Professor Lee was ranked as the most published finance professor worldwide during 1953-2002. ..Professor Alice C. Lee is an Assistant Professor of Finance at San Francisco State University. She has a div作者: 使高興 時間: 2025-3-27 13:40 作者: 最高峰 時間: 2025-3-27 21:28 作者: 反復(fù)無常 時間: 2025-3-27 23:24
Bruce C. Berndt,George E. Andrews Kong, China and the United States for the past three decades. In the winter 2005 issue of the Journal of Finance Literature, Professor Lee was ranked as the most published finance professor worldwide during 1953-2002. ..Professor Alice C. Lee is an Assistant Professor of Finance at San Francisco State University. She has a div978-0-387-26336-6作者: 運動吧 時間: 2025-3-28 02:17 作者: 保留 時間: 2025-3-28 07:51
Introduction, arrange all this disparate material into chapters for each of the proposed volumes. For a history and general description of Ramanujan’s lost notebook, readers are advised to read the introduction to our first book [31].作者: intercede 時間: 2025-3-28 11:05
Theta Function Identities,n how theta functions make perhaps unexpected appearances in .-series identities. Readers who continue to read the remainder of this volume will observe that theta functions and their identities are inextricably intertwined with Eisenstein series.作者: Truculent 時間: 2025-3-28 16:30 作者: voluble 時間: 2025-3-28 20:44
Partial Theta Functions,from the classical Jacobi theta function ., we have chosen to name the series in (6.1.1) .. We have chosen the designation partial theta functions, in contrast with L.J. Rogers’s “false theta functions” discussed in Chapters 9 and 11 of our first volume [31, pp. 227–239, 256–259].作者: innate 時間: 2025-3-28 23:28
Special Identities,The first four identities to be examined have previously been proved [20] by relating them to the theory of Durfee rectangles [13]. We provide an alternative development based on functional equations in Section 7.2.作者: 殘暴 時間: 2025-3-29 06:17 作者: BARGE 時間: 2025-3-29 10:11
,Ramanujan’s Cubic Analogue of the Classical Ramanujan–Weber Class Invariants, elegant values of ., for . ≡ 1 (mod 8). The quantity . can be thought of as an analogue in Ramanujan’s cubic theory of elliptic functions [57, Chapter 33] of the classical Ramanujan–Weber class invariant Gn, which is defined by . where . and . is any positive rational number.作者: 指數(shù) 時間: 2025-3-29 13:20 作者: 斥責(zé) 時間: 2025-3-29 15:53 作者: arsenal 時間: 2025-3-29 22:05
,Eisenstein Series and Approximations to π, To the right of each integer, Ramanujan recorded a linear equation in .. and ... Although Ramanujan did not indicate the definitions of . and ., we can easily (and correctly) ascertain that . and . are the Eisenstein series . and ., where .. To the right of each equation in .. and .., Ramanujan ent作者: Confound 時間: 2025-3-30 01:57
iscusses q-series, Eisenstein series, and theta functions.InThis 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, contain作者: Gobble 時間: 2025-3-30 07:18 作者: Demonstrate 時間: 2025-3-30 09:35 作者: Factual 時間: 2025-3-30 14:17
Book 2009t 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作者: 盲信者 時間: 2025-3-30 18:50 作者: 罵人有污點 時間: 2025-3-31 00:46 作者: Cultivate 時間: 2025-3-31 02:35 作者: 廣口瓶 時間: 2025-3-31 05:44
Bruce C. Berndt,George E. Andrewsons.Comprised of over 1000 individual definitions and chapteThe Encyclopedia of Finance, Second Edition, comprised of over 1000 individual definitions and chapters, is the most comprehensive and up-to-date resource in the field, integrating the most current terminology, research, theory, and practic作者: 小樣他閑聊 時間: 2025-3-31 10:28 作者: hermitage 時間: 2025-3-31 16:51 作者: 前奏曲 時間: 2025-3-31 21:09 作者: obstinate 時間: 2025-4-1 00:10
Bruce C. Berndt,George E. Andrewsons.Comprised of over 1000 individual definitions and chapteThe Encyclopedia of Finance, Second Edition, comprised of over 1000 individual definitions and chapters, is the most comprehensive and up-to-date resource in the field, integrating the most current terminology, research, theory, and practic
