Stieltjes%E2%80%93Wigert%20polynomials
(0.003 seconds)
1—10 of 335 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: 31.15 Stieltjes Polynomials
§31.15 Stieltjes Polynomials
►§31.15(i) Definitions
… ►§31.15(ii) Zeros
… ► … ►§31.15(iii) Products of Stieltjes Polynomials
…6: 18.40 Methods of Computation
…
►
§18.40(ii) The Classical Moment Problem
… ►Having now directly connected computation of the quadrature abscissas and weights to the moments, what follows uses these for a Stieltjes–Perron inversion to regain . ►Stieltjes Inversion via (approximate) Analytic Continuation
… ►Histogram Approach
… ►Derivative Rule Approach
…7: 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).8: 25.2 Definition and Expansions
…
►
25.2.4
►where the Stieltjes constants are defined via
►
25.2.5
…
►
25.2.10
, .
►For see §24.2(i), and for see §24.2(iii).
…
9: 1.14 Integral Transforms
…
►