Special Functions of Mathematical Physics

1. Front Matter

   Pages i-xviii

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2. Foundations of the Theory of Special Functions

   • Arnold F. Nikiforov, Vasilii B. Uvarov

   Pages 1-19

3. The Classical Orthogonal Polynomials

   • Arnold F. Nikiforov, Vasilii B. Uvarov

   Pages 21-200

4. Bessel Functions

   • Arnold F. Nikiforov, Vasilii B. Uvarov

   Pages 201-251

5. Hypergeometric functions

   • Arnold F. Nikiforov, Vasilii B. Uvarov

   Pages 253-294

6. Solution of some problems of Mathematical Physics, Quantum Mechanics, and Numerical Analysis

   • Arnold F. Nikiforov, Vasilii B. Uvarov

   Pages 295-368

7. Back Matter

   Pages 369-427

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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.

• Bessel function
• gamma function
• Hypergeometric function
• integral
• Mathematica
• mathematical physics
• mechanics
• numerical analysis
• orthogonal polynomials
• quantum mechanics
• solution
• special function

• M.V. Keldish Institute of Applied Mathematics of the Academy of Sciences of the USSR, Moscow, USSR

  Arnold F. Nikiforov, Vasilii B. Uvarov

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