標(biāo)題: Titlebook: Ramanujan’s Notebooks; Part III Bruce C. Berndt Book 1991 Springer Science+Business Media New York 1991 Identity.equation.function.proof.t [打印本頁] 作者: Awkward 時(shí)間: 2025-3-21 16:13
書目名稱Ramanujan’s Notebooks影響因子(影響力)
作者: 顧客 時(shí)間: 2025-3-21 21:18
Modular Equations of Higher and Composite Degrees,nd 7 were derived. Modular equations of degrees 11, 13, 17, 19, 23, 31, 47, and 71 are established in this chapter. Also, modular equations of composite degree, or “mixed” modular equations, are studied. Most of the equations of the latter type involve four distinct moduli, and so we begin by defining such a modular equation.作者: 從容 時(shí)間: 2025-3-22 02:46
978-1-4612-6963-2Springer Science+Business Media New York 1991作者: jettison 時(shí)間: 2025-3-22 07:56 作者: 關(guān)節(jié)炎 時(shí)間: 2025-3-22 09:25
Eisenstein Series,Chapter 21 concludes the organized portion of Ramanujan’s second notebook; after Chapter 21, there are 100 pages of unorganized material. Chapter 21 constitutes only four pages and thus is the shortest chapter in the second notebook. Almost all of the previous chapters are twelve pages in length.作者: 羊齒 時(shí)間: 2025-3-22 15:20
http://image.papertrans.cn/r/image/821016.jpg作者: 甜瓜 時(shí)間: 2025-3-22 17:18
https://doi.org/10.1007/978-1-4612-0965-2Identity; equation; function; proof; theorem作者: 雄辯 時(shí)間: 2025-3-23 00:18 作者: nonchalance 時(shí)間: 2025-3-23 01:29 作者: Nebulizer 時(shí)間: 2025-3-23 06:33
The Jacobian Elliptic Functions,inued in Chapter 17 with an introduction to elliptic integrals and the compilation of a large catalog of series that can be evaluated in terms of elliptic function parameters. This chapter contains further series identities depending on the theory of elliptic functions. Such results are considerably作者: Carcinogen 時(shí)間: 2025-3-23 10:10
Modular Equations of Degrees 3, 5, and 7 and Associated Theta-Function Identities,in regard to Ramanujan’s methods of proof. Undoubtedly, many of the proofs given here are quite unlike those found by Ramanujan. He evidently possessed methods that we have been unable to discern. No hints whatsoever of his methods are provided by Ramanujan.作者: 沒有希望 時(shí)間: 2025-3-23 17:09
Modular Equations of Higher and Composite Degrees,nd 7 were derived. Modular equations of degrees 11, 13, 17, 19, 23, 31, 47, and 71 are established in this chapter. Also, modular equations of composite degree, or “mixed” modular equations, are studied. Most of the equations of the latter type involve four distinct moduli, and so we begin by defini作者: 結(jié)果 時(shí)間: 2025-3-23 20:42
Book 1991undertaken. In 1977, Berndt began the tasks of editing Ramanujan‘s notebooks. Proofs are provided to theorems not yet proven in previous literature, and many results are so startling and different that there are no results akin to them in the literature.作者: Palate 時(shí)間: 2025-3-24 01:45
iting was undertaken. In 1977, Berndt began the tasks of editing Ramanujan‘s notebooks. Proofs are provided to theorems not yet proven in previous literature, and many results are so startling and different that there are no results akin to them in the literature.978-1-4612-6963-2978-1-4612-0965-2作者: uveitis 時(shí)間: 2025-3-24 05:58 作者: 沒有貧窮 時(shí)間: 2025-3-24 06:55 作者: poliosis 時(shí)間: 2025-3-24 11:17
Fundamental Properties of Elliptic Functions,classical notation and terminology from the theory of elliptic functions and integrals. In Section 6, we identify the functions and parameters employed by Ramanujan with the more familiar notations in the theory of elliptic functions.作者: leniency 時(shí)間: 2025-3-24 17:58
The Jacobian Elliptic Functions,ptic function parameters. This chapter contains further series identities depending on the theory of elliptic functions. Such results are considerably fewer in number here than in Chapter 17 and generally are more difficult to prove. In particular, see Sections 4-7.作者: Veneer 時(shí)間: 2025-3-24 23:00
Book 1991ical results without proofs in notebooks. Upon Ramanujan‘s death in 1920, G.H. Hardy strongly urged that Ramanujan‘s notebooks be published and edited. The English mathematicians G.N. Watson and B.M. Wilson began this task in 1929, but although they devoted nearly ten years to the project, the work 作者: Institution 時(shí)間: 2025-3-25 00:56
opics 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: flourish 時(shí)間: 2025-3-25 03:25
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: conscience 時(shí)間: 2025-3-25 07:52
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: characteristic 時(shí)間: 2025-3-25 13:54
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: phytochemicals 時(shí)間: 2025-3-25 16:32 作者: Handedness 時(shí)間: 2025-3-25 20:43
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: Tortuous 時(shí)間: 2025-3-26 01:13 作者: plasma 時(shí)間: 2025-3-26 06:54 作者: moratorium 時(shí)間: 2025-3-26 10:51 作者: 碌碌之人 時(shí)間: 2025-3-26 16:34 作者: 谷類 時(shí)間: 2025-3-26 20:29 作者: dandruff 時(shí)間: 2025-3-26 23:27 作者: 我怕被刺穿 時(shí)間: 2025-3-27 02:56 作者: 碎片 時(shí)間: 2025-3-27 08:48
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 i978-3-319-17885-1作者: 令人心醉 時(shí)間: 2025-3-27 11:17 作者: 加入 時(shí)間: 2025-3-27 16:02 作者: forecast 時(shí)間: 2025-3-27 19:08
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: 一大塊 時(shí)間: 2025-3-28 01:26
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: Commission 時(shí)間: 2025-3-28 06:04
1613-3382 e most recalcitrant contaminants. Nevertheless, bioremediation is a rapidly advancing field and new bio-based remedial technologies are continuing to emerge.978-3-642-05908-7978-3-662-05794-0Series ISSN 1613-3382 Series E-ISSN 2196-4831 作者: 死亡 時(shí)間: 2025-3-28 09:24 作者: Seizure 時(shí)間: 2025-3-28 11:13 作者: 緊張過度 時(shí)間: 2025-3-28 18:28
Book 2004ctive, though a minority feel are too morbid to deserve detailed attention. This book is designed to offer a framework for studying historic burial ground monuments, and contains a certain amount of information regarding below-ground archaeology, as some projects will involve the study of both. More
