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From Gauss to Painlevé

149,79 €*

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Produktnummer: 18bf6ab7042c8a4f4bae2a78fdbd0a5876
Autor: Iwasaki, Katsunori Kimura, Hironobu Shimemura, Shun Yoshida, Masaaki
Themengebiete: Excel Mathematica Microsoft Access Monodromy differential equation equation form function functions group
Veröffentlichungsdatum: 12.06.2012
EAN: 9783322901651
Sprache: Englisch
Seitenzahl: 347
Produktart: Kartoniert / Broschiert
Verlag: Vieweg & Teubner
Untertitel: A Modern Theory of Special Functions
Produktinformationen "From Gauss to Painlevé"
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 70 years later that they were used in physics in order to describe the correlation function of the two dimen sional Ising model. During the last 15 years, more and more people have become interested in these equations, and nice algebraic, geometric and analytic properties were found.
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