continuous%20q-ultraspherical%20polynomials
(0.005 seconds)
1—10 of 353 matching pages
1: 31.5 Solutions Analytic at Three Singularities: Heun Polynomials
§31.5 Solutions Analytic at Three Singularities: Heun Polynomials
… ►
31.5.2
►is a polynomial of degree , and hence a solution of (31.2.1) that is analytic at all three finite singularities .
These solutions are the Heun polynomials.
…
2: 35.4 Partitions and Zonal Polynomials
§35.4 Partitions and Zonal Polynomials
… ►Normalization
… ►Orthogonal Invariance
… ►Summation
… ►Mean-Value
…3: 24.1 Special Notation
…
►
Bernoulli Numbers and Polynomials
►The origin of the notation , , is not clear. … ►Euler Numbers and Polynomials
… ►The notations , , as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …4: 18.3 Definitions
§18.3 Definitions
… ►For expressions of ultraspherical, Chebyshev, and Legendre polynomials in terms of Jacobi polynomials, see §18.7(i). …For explicit power series coefficients up to for these polynomials and for coefficients up to for Jacobi and ultraspherical polynomials see Abramowitz and Stegun (1964, pp. 793–801). … ►Bessel polynomials
►Bessel polynomials are often included among the classical OP’s. …5: 20 Theta Functions
Chapter 20 Theta Functions
…6: 6.16 Mathematical Applications
7: 18.1 Notation
…
►
…
►
…
►
►
►
…
Continuous Hahn: .
Continuous Dual Hahn: .
Continuous -Ultraspherical: .
Continuous -Hermite: .
Continuous -Hermite:
8: 18.29 Asymptotic Approximations for -Hahn and Askey–Wilson Classes
§18.29 Asymptotic Approximations for -Hahn and Askey–Wilson Classes
►Ismail (1986) gives asymptotic expansions as , with and other parameters fixed, for continuous -ultraspherical, big and little -Jacobi, and Askey–Wilson polynomials. …For Askey–Wilson the leading term is given by … ►For a uniform asymptotic expansion of the Stieltjes–Wigert polynomials, see Wang and Wong (2006). ►For asymptotic approximations to the largest zeros of the -Laguerre and continuous -Hermite polynomials see Chen and Ismail (1998).9: 18.25 Wilson Class: Definitions
…
►The Wilson class consists of two discrete families (Racah and dual Hahn) and two continuous families (Wilson and continuous dual Hahn).
…
►Under certain conditions on their parameters the orthogonality range for the Wilson polynomials and continuous dual Hahn polynomials is , where is a specific finite set, e.
…
►
§18.25(ii) Weights and Standardizations: Continuous Cases
… ►Continuous Dual Hahn
… ►Table 18.25.2 provides the leading coefficients (§18.2(iii)) for the Wilson, continuous dual Hahn, Racah, and dual Hahn polynomials. …10: Bibliography F
…
►
Multivariate Calculation. Use of the Continuous Groups.
Springer Series in Statistics, Springer-Verlag, New York.
…
►
…
►
Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
…
►
From continuous to discrete Painlevé equations.
J. Math. Anal. Appl. 180 (2), pp. 342–360.
…
►
On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
…