標題: Titlebook: Ramanujan’s Notebooks; Part IV Bruce C. Berndt Book 1994 Springer Science+Business Media, LLC, part of Springer Nature 1994 Ramanujan.calcu [打印本頁] 作者: crusade 時間: 2025-3-21 16:16
書目名稱Ramanujan’s Notebooks影響因子(影響力)
作者: Genteel 時間: 2025-3-21 23:04 作者: AMBI 時間: 2025-3-22 03:59 作者: Mortar 時間: 2025-3-22 06:18
Bruce C. Berndtith new content on emerging topics such as big data.Equips r.New In This Edition: This second edition of the Encyclopedia of GIS includes 30% to 50% new content. It provides up-to-date information on emerging topics such as spatial big data, smart-phone GIS, urban computing and mobile recommender sy作者: Mindfulness 時間: 2025-3-22 12:35 作者: 會議 時間: 2025-3-22 15:12
Bruce C. Berndtopics such as spatial big data, smart-phone GIS, urban computing and mobile recommender systems. It also expands the first edition’s rich set of GIS-related commercial and societal applications such as geo-targeting, geo-fencing and understanding climate changes, while enabling more comprehensive co作者: 來就得意 時間: 2025-3-22 20:12 作者: Pericarditis 時間: 2025-3-22 22:21 作者: 極端的正確性 時間: 2025-3-23 05:03
Bruce C. Berndtopics such as spatial big data, smart-phone GIS, urban computing and mobile recommender systems. It also expands the first edition’s rich set of GIS-related commercial and societal applications such as geo-targeting, geo-fencing and understanding climate changes, while enabling more comprehensive co作者: 彎腰 時間: 2025-3-23 05:45 作者: 顛簸地移動 時間: 2025-3-23 10:19
Bruce C. Berndtith new content on emerging topics such as big data.Equips r.New In This Edition: This second edition of the Encyclopedia of GIS includes 30% to 50% new content. It provides up-to-date information on emerging topics such as spatial big data, smart-phone GIS, urban computing and mobile recommender sy作者: 侵略 時間: 2025-3-23 14:35
Bruce C. Berndtopics such as spatial big data, smart-phone GIS, urban computing and mobile recommender systems. It also expands the first edition’s rich set of GIS-related commercial and societal applications such as geo-targeting, geo-fencing and understanding climate changes, while enabling more comprehensive co作者: incarcerate 時間: 2025-3-23 20:23 作者: Mettle 時間: 2025-3-23 23:06 作者: 沖突 時間: 2025-3-24 04:35
iscoveries without proofs in notebooks. Although many of his results were already found in the literature, most were not. Almost a decade after Ramanujan‘s death in 1920, G.N. Watson and B.M. Wilson began to edit Ramanujan‘s notebooks, but they never completed the task. A photostat edition, with no 作者: MIRE 時間: 2025-3-24 09:38 作者: 神刊 時間: 2025-3-24 14:08 作者: BACLE 時間: 2025-3-24 16:15 作者: Efflorescent 時間: 2025-3-24 19:22
Number Theory,ing of 33 pages. Most of the material on these 133 pages was probably recorded in approximately the years 1912-1914, before Ramanujan departed for Cambridge. However, there is some evidence, especially from the material on number theory, that several entries in the third notebook were recorded in England.作者: Conserve 時間: 2025-3-25 02:19 作者: 東西 時間: 2025-3-25 03:42 作者: 客觀 時間: 2025-3-25 10:10
-Series,rmulas given in Entries 6–8. Thus, in this chapter, only eight results are proved. Additional .-analysis can be found in Chapter 32, entitled Continued Fractions (Berndt [9]), or in the memoir of Andrews, Berndt, Jacobsen, and Lamphere [1]. Further related material can be found in Chapter 25 on theta-functions.作者: Anticlimax 時間: 2025-3-25 13:00 作者: 向外供接觸 時間: 2025-3-25 19:33
Number Theory,lts on number theory found in the notebooks lie in the 100 unorganized pages at the end of the second notebook and in the short third notebook consisting of 33 pages. Most of the material on these 133 pages was probably recorded in approximately the years 1912-1914, before Ramanujan departed for Cam作者: Induction 時間: 2025-3-25 20:15 作者: craving 時間: 2025-3-26 02:42
Theta-Functions and Modular Equations,s. However, the unorganized pages in the second and third notebooks also embrace a large amount of Ramanujan’s findings on these topics. In this chapter, we shall discuss most of this material. In Chapter 33 (Part V [9]), we relate Ramanujan’s fascinating theories of elliptic functions and modular e作者: 強所 時間: 2025-3-26 05:38
-Series,ch is almost completely devoted to .-series, it is surprising that the unorganized portion of the second notebook and the third notebook contain only a small amount of material on .-series. In fact, only five identities are to be found here (Entries 1–5 below). More interesting are the asymptotic fo作者: frivolous 時間: 2025-3-26 10:36
Integrals,ghted by several elegant asymptotic expansions of integrals. In this chapter, we examine the nearly 50 results on integrals appearing in the 100 pages at the end of the second notebook, and in the 33-page third notebook.作者: 菊花 時間: 2025-3-26 15:19
Special Functions,e first ten entries concern the gamma function. All ten entries are either known results or can easily be derived from standard theorems on the gamma function. The next four theorems arise from the theory of Bessel functions. These four theorems also are either classical or can be simply deduced fro作者: Reverie 時間: 2025-3-26 17:04
Partial Fraction Expansions,s lie in Chapters 14 and 18 and in the unorganized pages at the end of the second notebook. See our books [4] and [6] for accounts of the material in Chapters 14 and 18, respectively. In this chapter, we prove the 15 partial fraction decompositions found in the unorganized pages of the second notebo作者: Indicative 時間: 2025-3-27 00:00 作者: delegate 時間: 2025-3-27 01:57
Book 1994d notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the note作者: glans-penis 時間: 2025-3-27 08:28
the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the note978-1-4612-6932-8978-1-4612-0879-2作者: GLUE 時間: 2025-3-27 10:45
Bruce C. Berndtcomers to the field with principles as well as applications. With an accessible breadth of content and intuitive A-Z organization, this new edition of the encyclopedia is an invaluable reference for newcomers to the field of?GIS, as well as researchers, students, developers and professionals who are作者: critique 時間: 2025-3-27 17:29
Bruce C. Berndtomers to the field with principles as well as applications. With an accessible breadth of contentand intuitive A-Z organization, this new edition of the encyclopedia is an invaluable reference for newcomers to the field of?GIS, as well as researchers, students, developers and professionals who are i作者: membrane 時間: 2025-3-27 21:45 作者: PAN 時間: 2025-3-28 00:41 作者: 毗鄰 時間: 2025-3-28 04:11
Bruce C. Berndtomers to the field with principles as well as applications. With an accessible breadth of contentand intuitive A-Z organization, this new edition of the encyclopedia is an invaluable reference for newcomers to the field of?GIS, as well as researchers, students, developers and professionals who are i作者: interpose 時間: 2025-3-28 08:28 作者: 解開 時間: 2025-3-28 12:16 作者: glomeruli 時間: 2025-3-28 16:07
Bruce C. Berndtcontentand intuitive A-Z organization, this new edition of the encyclopedia is an invaluable reference for newcomers to the field of?GIS, as well as researchers, students, developers and professionals who are i978-3-319-17885-1作者: Resistance 時間: 2025-3-28 18:44
Bruce C. Berndtcontentand intuitive A-Z organization, this new edition of the encyclopedia is an invaluable reference for newcomers to the field of?GIS, as well as researchers, students, developers and professionals who are i978-3-319-17885-1作者: 廚房里面 時間: 2025-3-29 01:56
Bruce C. Berndtcontentand intuitive A-Z organization, this new edition of the encyclopedia is an invaluable reference for newcomers to the field of?GIS, as well as researchers, students, developers and professionals who are i978-3-319-17885-1作者: Cupping 時間: 2025-3-29 05:15 作者: deriver 時間: 2025-3-29 09:22
Bruce C. Berndtcontentand intuitive A-Z organization, this new edition of the encyclopedia is an invaluable reference for newcomers to the field of?GIS, as well as researchers, students, developers and professionals who are i978-3-319-17885-1作者: Mortar 時間: 2025-3-29 11:46 作者: gustation 時間: 2025-3-29 18:00
Introduction,Ramanujan built many castles. Although some may have been lost, most were preserved. Since his death in 1920, many mathematicians have been constructing the foundations for these magnificent structures. We continue this task in the present volume.作者: cathartic 時間: 2025-3-29 23:35
Inversion Formulas for the Lemniscate and Allied Functions,On pages 283, 285, and 286 in his second notebook [22], Ramanujan states ten inversion formulas for series. As an example, we quote (in a somewhat more compact notation) the entry at the top of page 285.
