Orthogonal Polynomials and Special Functions (CBMS-NSF Regional Conference Series in Applied Mathematics, Series Number 21)

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. 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