Special functions of mathematical physics : a unified introduction with applications

著者

書誌事項

Special functions of mathematical physics : a unified introduction with applications

Arnold F. Nikiforov, Vasilii B. Uvarov ; translated from the Russian by Ralph P. Boas

Springer Basel AG, 1988

  • : pbk

タイトル別名

Special'nye funkcii matematičeskoj fiziki

Spet︠s︡ialʹnye funkt︠s︡ii matematicheskoĭ fiziki

大学図書館所蔵 件 / 全1件

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注記

"Originally published as Special'nye funkcii matematičeskoj fiziki by Science, Moscow, 1978."--T. p. verso

Translation of: Spet︠s︡ialʹnye funkt︠s︡ii matematicheskoĭ fiziki

"Originally published by Birkhäuser Verlag Basel in 1988."--T. p. verso

Includes bibliographical references (p. 416-419) and index

内容説明・目次

内容説明

With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan tum mechanics. We have not attempted to provide the most extensive collec tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics. For the American edition we have been able to improve a number of proofs; in particular, we have given a new proof of the basic theorem (3). This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type (12, 13). Several sections have been simplified and contain new material. We believe that this is the first time that the theory of classical or thogonal polynomials of a discrete variable on both uniform and nonuniform lattices has been given such a coherent presentation, together with its various applications in physics.

目次

I Foundations of the theory of special functions.- II The classical orthogonal polynomials.- III Bessel functions.- IV Hypergeometric functions.- V Solution of some problems of mathematical physics, quantum mechanics and numerical analysis.- Appendices.- A. The Gamma function.- B. Analytic properties and asymptotic representations of Laplace integrals.- Basic formulas.- List of tables.- References.- Index of notations.- List of figures.

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