CiNii 図書 - Hypergeometric functions and their applications

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A wide range of problems exists in classical and quantum physics, engi neering, and applied mathematics in which special functions arise. The procedure followed in most texts on these topics (e. g. , quantum mechanics, electrodynamics, modern physics, classical mechanics, etc. ) is to formu late the problem as a differential equation that is related to one of several special differential equations (Hermite's, Bessel's, Laguerre's, Legendre's, etc. ).

1 Special Functions in Applied Mathematics.- 2 Differential Equations and Special Functions.- 3 The Confluent Hypergeometric Function.- 4 Problems in Two Dimensions.- 5 The Central Force Problem in Quantum Mechanics.- 6 The Radial Equation for Central Force Fields.- 7 Complex Analysis.- 8 Applications of Contour Integrals.- 9 Alternate Forms for Special Functions.- 10 Integral Representations of Special Functions.- 11 Generating Functions and Recursion Formulas.- 12 Orthogonal Functions.

巻冊次: : Berlin ISBN 9783540975588

内容説明

This textbook is intended as a supplement to courses in classical or quantum mechanics, electrodynamics or any other physics course in which the reader encounters hypergeometric functions. It aims to serve as a reference for hypergeometric functions, for the relationship of hypergeometric functions to special functions, and for those areas of special functions which are useful in physics. The reader should have completed two or three semesters of calculus and should also have some knowledge of Schrodinger's equations. Courses at the intermediate level in classical mechanics and/or electricity and magnetism are also desirable but not essential.

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Hypergeometric functions and their applications

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