Orthogonal Polynomials and Special Functions

Richard Askey9780898710182, 0898710189

Originally presented as lectures, the theme of this volume is that one studies orthogonal polynomials and special functions not for their own sake, but to be able to use them to solve problems. The author presents problems suggested by the isometric embedding of projective spaces in other projective spaces, by the desire to construct large classes of univalent functions, by applications to quadrature problems, and theorems on the location of zeros of trigonometric polynomials. There are also applications to combinatorial problems, statistics, and physical problems.

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Table of contents :
Orthogonal Polynomials and Special Functions……Page 1
Contents……Page 9
Preface……Page 10
LECTURE 1 Classical Results for Trigonometric Polynomials and Fourier Series and Other Isolated Results……Page 14
LECTURE 2 Jacob! Polynomial Series……Page 20
LECTURE 3 Fractional Integrals and Hypergeometric Functions……Page 32
LECTURE 4 Addition Formulas……Page 42
LECTURE 5 Linearization of Products……Page 52
LECTURE 6 Rational Functions with Positive Power Series Coefficients……Page 60
LECTURE 7 Connection Coefficients……Page 70
LECTURE 8 Positive Sums……Page 84
LECTURE 9 More Positive Sums and Applications……Page 96
LECTURE 10 Suggestions for Further Work……Page 106
References……Page 112