Ebook: 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. ).

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The book is intended as a supplement to courses in classical or quantum mechanics, electrodynamics, or any other physics course in which one encounters hypergeometric functions. It will 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 have some knowledge of Schr?dinger'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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The book is intended as a supplement to courses in classical or quantum mechanics, electrodynamics, or any other physics course in which one encounters hypergeometric functions. It will 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 have some knowledge of Schr?dinger's equations. Courses at the intermediate level in classical mechanics and/or electricity and magnetism are also desirable but not essential.
Content:
Front Matter....Pages i-xiv
Special Functions in Applied Mathematics....Pages 1-14
Differential Equations and Special Functions....Pages 15-40
The Confluent Hypergeometric Function....Pages 41-51
Problems in Two Dimensions....Pages 53-68
The Central Force Problem in Quantum Mechanics....Pages 69-80
The Radial Equation for Central Force Fields....Pages 81-98
Complex Analysis....Pages 99-128
Applications of Contour Integrals....Pages 129-153
Alternate Forms for Special Functions....Pages 155-169
Integral Representations of Special Functions....Pages 171-196
Generating Functions and Recursion Formulas....Pages 197-212
Orthogonal Functions....Pages 213-244
Back Matter....Pages 245-250

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The book is intended as a supplement to courses in classical or quantum mechanics, electrodynamics, or any other physics course in which one encounters hypergeometric functions. It will 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 have some knowledge of Schr?dinger's equations. Courses at the intermediate level in classical mechanics and/or electricity and magnetism are also desirable but not essential.
Content:
Front Matter....Pages i-xiv
Special Functions in Applied Mathematics....Pages 1-14
Differential Equations and Special Functions....Pages 15-40
The Confluent Hypergeometric Function....Pages 41-51
Problems in Two Dimensions....Pages 53-68
The Central Force Problem in Quantum Mechanics....Pages 69-80
The Radial Equation for Central Force Fields....Pages 81-98
Complex Analysis....Pages 99-128
Applications of Contour Integrals....Pages 129-153
Alternate Forms for Special Functions....Pages 155-169
Integral Representations of Special Functions....Pages 171-196
Generating Functions and Recursion Formulas....Pages 197-212
Orthogonal Functions....Pages 213-244
Back Matter....Pages 245-250
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