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標題: Titlebook: Ramanujan’s Notebooks; Part II Bruce C. Berndt Book 1989 Springer-Verlag New York Inc. 1989 Finite.Mathematica.Modular form.integral.proof [打印本頁]

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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
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Bruce C. Berndt 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 are978-3-319-23519-6
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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 are978-3-319-23519-6
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o prove it. Not only are the results fascinating, but, for the most part, Ramanujan‘s methods remaina mystery. Much work still needs to be done. We hope readers will strive to discover Ramanujan‘s thoughts and further develop his beautiful ideas.978-1-4612-8865-7978-1-4612-4530-8
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Infinite Series,l results in Chapter 14, as well as many others as well, aries from a general transformation formula for a large class of analytic Eisenstein series. It should be emphasized, however, that Chapter 14 also contains many other types of results.
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his results were already in the literature, more were not. Almost a decade after Ramanujan‘s death in 1920, G.N. Watson and B.M. Wilson began to edit his notebooks but never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bomba
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Hypergeometric Series, I,rresponds to Chapter 10 of the second notebook, is connected primarily with hypergeometric series. It should be emphasized that Hardy gave only a brief survey of Chapter 12; this chapter contains many interesting results not mentioned by Hardy, and Chapter 10 of the second notebook possesses materia
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Continued Fractions,ely; I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written down by a mathematician of the highest class. They must be true because, if they were not true, no one would have had the imagination to invent them.” These comments
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Integrals and Asymptotic Expansions,sive.” Later he added that Ramanujan’s definite integral formulae “are still interesting and will repay a careful analysis” [9, p. 186]. Indeed, a dismissal of Ramanujan’s contributions to intergration would have beed decidedly premature. First, we might recall that this first letter contained sever
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Book 1989s were already in the literature, more were not. Almost a decade after Ramanujan‘s death in 1920, G.N. Watson and B.M. Wilson began to edit his notebooks but never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957.
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https://doi.org/10.1007/978-1-4612-4530-8Finite; Mathematica; Modular form; integral; proof
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Asymptotic Expansions and Modular Forms, notebook, Chapter 15 contains more disparate topics than the remaining chapters. Ramanujan appears to have collected here several “odds and ends.” While much of the materials is fascinating, a few part have little substance.
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topics 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 c
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topics 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 c
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Bruce C. Berndttopics 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 c
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Bruce C. Berndtstandards.Provides a comprehensive and authoritative treatme.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 s
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standards.Provides a comprehensive and authoritative treatme.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 s
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2194-3125 for the Psychological Study of Social Issues and the International Society of Political Psychology, he helped to foster social science efforts to make for a more peaceful world.978-3-319-15442-8978-3-319-15443-5Series ISSN 2194-3125 Series E-ISSN 2194-3133




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