Hypergeometric Functions and Their Applications

1. Front Matter

   Pages i-xiv

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2. Special Functions in Applied Mathematics

   • James B. Seaborn

   Pages 1-14

3. Differential Equations and Special Functions

   • James B. Seaborn

   Pages 15-40

4. The Confluent Hypergeometric Function

   • James B. Seaborn

   Pages 41-51

5. Problems in Two Dimensions

   • James B. Seaborn

   Pages 53-68

6. The Central Force Problem in Quantum Mechanics

   • James B. Seaborn

   Pages 69-80

7. The Radial Equation for Central Force Fields

   • James B. Seaborn

   Pages 81-98

8. Complex Analysis

   • James B. Seaborn

   Pages 99-128

9. Applications of Contour Integrals

   • James B. Seaborn

   Pages 129-153

10. Alternate Forms for Special Functions

    • James B. Seaborn

    Pages 155-169

11. Integral Representations of Special Functions

    • James B. Seaborn

    Pages 171-196

12. Generating Functions and Recursion Formulas

    • James B. Seaborn

    Pages 197-212

13. Orthogonal Functions

    • James B. Seaborn

    Pages 213-244

14. Back Matter

    Pages 245-250

    PDF

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. ).

• applied mathematics
• calculus
• complex analysis
• differential equation
• mechanics
• quantum mechanics

• Department of Physics, University of Richmond, USA

  James B. Seaborn

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