##
**Orthogonal polynomials. 4th ed.**
*(English)*
Zbl 0305.42011

Colloquium Publications. American Mathematical Society 23. Providence, RI: American Mathematical Society (AMS). xiii, 432 p. (1975).

### MSC:

42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |

33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |

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\textit{G. Szegö}, Orthogonal polynomials. 4th ed. Providence, RI: American Mathematical Society (AMS) (1975; Zbl 0305.42011)

### Digital Library of Mathematical Functions:

§18.10(iii) Contour Integral Representations ‣ §18.10 Integral Representations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials§18.10(ii) Laplace-Type Integral Representations ‣ §18.10 Integral Representations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.10(i) Dirichlet–Mehler-Type Integral Representations ‣ §18.10 Integral Representations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.11(ii) Formulas of Mehler–Heine Type ‣ §18.11 Relations to Other Functions ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.12 Generating Functions ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.14(iii) Local Maxima and Minima ‣ §18.14 Inequalities ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.14(i) Upper Bounds ‣ §18.14 Inequalities ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.15(ii) Ultraspherical ‣ §18.15 Asymptotic Approximations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.15(iii) Legendre ‣ §18.15 Asymptotic Approximations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.15(iii) Legendre ‣ §18.15 Asymptotic Approximations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.15(ii) Ultraspherical ‣ §18.15 Asymptotic Approximations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.15(ii) Ultraspherical ‣ §18.15 Asymptotic Approximations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.15(i) Jacobi ‣ §18.15 Asymptotic Approximations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.15(iv) Laguerre ‣ §18.15 Asymptotic Approximations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.15(v) Hermite ‣ §18.15 Asymptotic Approximations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.16(ii) Jacobi ‣ §18.16 Zeros ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.16(iv) Laguerre ‣ §18.16 Zeros ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.16(v) Hermite ‣ §18.16 Zeros ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.16(vi) Additional References ‣ §18.16 Zeros ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.17(viii) Other Integrals ‣ §18.17 Integrals ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.18(i) Series Expansions of Arbitrary Functions ‣ §18.18 Sums ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.18(viii) Other Sums ‣ §18.18 Sums ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.1(iii) Other Notations ‣ §18.1 Notation ‣ Notation ‣ Chapter 18 Orthogonal Polynomials

§18.2(iii) Normalization ‣ §18.2 General Orthogonal Polynomials ‣ General Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.2(iv) Recurrence Relations ‣ §18.2 General Orthogonal Polynomials ‣ General Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

Orthogonality on Finite Point Sets ‣ §18.2(i) Definition ‣ §18.2 General Orthogonal Polynomials ‣ General Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.2(v) Christoffel–Darboux Formula ‣ §18.2 General Orthogonal Polynomials ‣ General Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.31 Bernstein–Szegő Polynomials ‣ Other Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.33(iii) Connection with OP’s on the Line ‣ §18.33 Polynomials Orthogonal on the Unit Circle ‣ Other Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.33(ii) Recurrence Relations ‣ §18.33 Polynomials Orthogonal on the Unit Circle ‣ Other Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.33(i) Definition ‣ §18.33 Polynomials Orthogonal on the Unit Circle ‣ Other Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

Table 18.3.1 ‣ §18.3 Definitions ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions ‣ §18.5 Explicit Representations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.5(ii) Rodrigues Formulas ‣ §18.5 Explicit Representations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.5(i) Trigonometric Functions ‣ §18.5 Explicit Representations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.6(i) Symmetry and Special Values ‣ §18.6 Symmetry, Special Values, and Limits to Monomials ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.7(iii) Limit Relations ‣ §18.7 Interrelations and Limit Relations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.7(ii) Quadratic Transformations ‣ §18.7 Interrelations and Limit Relations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.7(i) Linear Transformations ‣ §18.7 Interrelations and Limit Relations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.8 Differential Equations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.9(iii) Derivatives ‣ §18.9 Recurrence Relations and Derivatives ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.9(ii) Contiguous Relations in the Parameters and the Degree ‣ §18.9 Recurrence Relations and Derivatives ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

§18.9(i) Recurrence Relations ‣ §18.9 Recurrence Relations and Derivatives ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials

Chapter 18 Orthogonal Polynomials

Notations P ‣ Notations