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Home > Art, Film & Photography > Q-Analogs: Stirling Number, Mock Modular Form, Theta Function, Generalizations of the Derivative, Q-Analog, Basic Hypergeometric Series, Gaussian Binomial Coef
Q-Analogs: Stirling Number, Mock Modular Form, Theta Function, Generalizations of the Derivative, Q-Analog, Basic Hypergeometric Series, Gaussian Binomial Coef

Q-Analogs: Stirling Number, Mock Modular Form, Theta Function, Generalizations of the Derivative, Q-Analog, Basic Hypergeometric Series, Gaussian Binomial Coef


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 22. Chapters: Stirling number, Mock modular form, Theta function, Generalizations of the derivative, Q-analog, Basic hypergeometric series, Gaussian binomial coefficient, Q-Pochhammer symbol, Q-Vandermonde identity, Rogers-Ramanujan identities, Lambert series, Tsallis entropy, Q-derivative, Euler function, Ramanujan theta function, Jackson integral, Elliptic gamma function, Q-difference polynomial, Q-exponential, Q-gamma function, LLT polynomial, Q-theta function. Excerpt: In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight 1/2. The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 letter to G. H. Hardy and in his lost notebook. Ramanujan's own definition of mock theta functions is notoriously vague, and it was an open problem for many years to find a better definition. This was finally solved by Sander Zwegers (2001, 2002), who discovered that adding certain non-holomorphic functions to them turns them into harmonic weak Maass forms. Ramanujan's 1920 Jan 12 letter to Hardy, reprinted in (Ramanujan 2000, Appendix II), listed 17 examples of functions that he called mock theta functions, and his lost notebook (Ramanujan 1988) contained several more examples. (Ramanujan used the term "theta function" for what today would be called a modular form.) Ramanujan pointed out that they have an asymptotic expansion at the cusps, similar to that of modular forms of weight 1/2, possibly with poles at cusps, but cannot be expressed in terms of "ordinary" theta functions. In a notoriously obscure definition, he called functions with similar properties "mock theta functions." No better definition was found for many years, until Zwegers discovered the connection with weak Maass forms. Ramanujan ...


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Product Details
  • ISBN-13: 9781155773766
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 24
  • Spine Width: 1 mm
  • Weight: 64 gr
  • ISBN-10: 1155773764
  • Publisher Date: 12 Oct 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Stirling Number, Mock Modular Form, Theta Function, Generalizations of the Derivative, Q-Analog, Basic Hypergeometric Series, Gaussian Binomial Coef
  • Width: 189 mm


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