Hahn%20polynomials
(0.002 seconds)
1—10 of 316 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: 18.19 Hahn Class: Definitions
§18.19 Hahn Class: Definitions
… ►Hahn, Krawtchouk, Meixner, and Charlier
… ►Continuous Hahn
… ► … ►A special case of (18.19.8) is .6: 18.21 Hahn Class: Interrelations
§18.21 Hahn Class: Interrelations
►§18.21(i) Dualities
►Duality of Hahn and Dual Hahn
… ►§18.21(ii) Limit Relations and Special Cases
… ►Hahn Jacobi
…7: 18.1 Notation
8: 18.26 Wilson Class: Continued
…
►
Wilson Continuous Dual Hahn
… ►Wilson Continuous Hahn
… ►Racah Hahn
… ►Continuous Dual Hahn
… ►Dual Hahn
…9: 18.24 Hahn Class: Asymptotic Approximations
§18.24 Hahn Class: Asymptotic Approximations
►Hahn
►When the parameters and are fixed and the ratio is a constant in the interval (0,1), uniform asymptotic formulas (as ) of the Hahn polynomials can be found in Lin and Wong (2013) for in three overlapping regions, which together cover the entire complex plane. … ►Approximations in Terms of Laguerre Polynomials
… ►Similar approximations are included for Jacobi, Krawtchouk, and Meixner polynomials.10: 18.25 Wilson Class: Definitions
…
►Table 18.25.1 lists the transformations of variable, orthogonality ranges, and parameter constraints that are needed in §18.2(i) for the Wilson polynomials
, continuous dual Hahn polynomials
, Racah polynomials
, and dual Hahn polynomials
.
…
►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.
…
►