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Titlebook: Ramanujan’s Notebooks; Part III Bruce C. Berndt Book 1991 Springer Science+Business Media New York 1991 Identity.equation.function.proof.t

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书目名称Ramanujan’s Notebooks
副标题Part III
编辑Bruce C. Berndt
视频video
图书封面Titlebook: Ramanujan’s Notebooks; Part III Bruce C. Berndt Book 1991 Springer Science+Business Media New York  1991 Identity.equation.function.proof.t
描述During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical 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 was never completed. In 1957, the Tata Institute of Fundamental Research in Bombay published a photostat edition of the notebooks, but no editing 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.
出版日期Book 1991
关键词Identity; equation; function; proof; theorem
版次1
doihttps://doi.org/10.1007/978-1-4612-0965-2
isbn_softcover978-1-4612-6963-2
isbn_ebook978-1-4612-0965-2
copyrightSpringer Science+Business Media New York 1991
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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.
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978-1-4612-6963-2Springer Science+Business Media New York 1991
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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.
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https://doi.org/10.1007/978-1-4612-0965-2Identity; equation; function; proof; theorem
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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
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