| 书目名称 | From Gauss to Painlevé | | 副标题 | A Modern Theory of S | | 编辑 | Katsunori Iwasaki,Hironobu Kimura,Masaaki Yoshida | | 视频video | | | 丛书名称 | Aspects of Mathematics | | 图书封面 |  | | 描述 | Preface The Gamma function, the zeta function, the theta function, the hyper geometric function, the Bessel function, the Hermite function and the Airy function, . . . are instances of what one calls special functions. These have been studied in great detail. Each of them is brought to light at the right epoch according to both mathematicians and physicists. Note that except for the first three, each of these functions is a solution of a linear ordinary differential equation with rational coefficients which has the same name as the functions. For example, the Bessel equation is the simplest non-trivial linear ordinary differential equation with an irreg ular singularity which leads to the theory of asymptotic expansion, and the Bessel function is used to describe the motion of planets (Kepler‘s equation). Many specialists believe that during the 21st century the Painleve functions will become new members of the community of special func tions. For any case, mathematics and physics nowadays already need these functions. The corresponding differential equations are non-linear ordinary differential equations found by P. Painleve in 1900 fqr purely mathematical reasons. It was only | | 出版日期 | Book 1991 | | 关键词 | Excel; Mathematica; Microsoft Access; Monodromy; differential equation; equation; form; function; functions; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-322-90163-7 | | isbn_softcover | 978-3-322-90165-1 | | isbn_ebook | 978-3-322-90163-7Series ISSN 0179-2156 | | issn_series | 0179-2156 | | copyright | Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig 1991 |
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发表于 2025-3-21 17:09:24
