zeros of polynomials

SearchAdvancedHelp

(0.004 seconds)

11—20 of 80 matching pages

11: 3.5 Quadrature

… ►

Table 3.5.2: Nodes and weights for the 10-point Gauss–Legendre formula.

► ►►

$\pm x_k$	$w_k$
…

►

►

Table 3.5.3: Nodes and weights for the 20-point Gauss–Legendre formula.

► ►►

$\pm x_k$	$w_k$
…

►

… ► … ►

Table 3.5.6: Nodes and weights for the 5-point Gauss–Laguerre formula.

► ►►

$x_k$		$w_k$
…

►

… ►The $p_n(x)$ are the monic Hermite polynomials $H_n\left(x\right)$ (§18.3). …

12: Bibliography Q

… ►

Asymptotic expansion of the Krawtchouk polynomials and their zeros. Comput. Methods Funct. Theory 4 (1), pp. 189–226.

ⓘ

External Links:

ISSN 1617-9447, FullText, MathReview (C. M. Joshi), ZentralBlatt (N. M. Temme)

Referenced by:

§18.24.

Encodings:

BibTeX

…

13: 18.29 Asymptotic Approximations for $q$-Hahn and Askey–Wilson Classes

… ►For a uniform asymptotic expansion of the Stieltjes–Wigert polynomials, see Wang and Wong (2006). ►For asymptotic approximations to the largest zeros of the $q$-Laguerre and continuous $q^{-1}$-Hermite polynomials see Chen and Ismail (1998).

14: 28.31 Equations of Whittaker–Hill and Ince

… ►The normalization is given by …

15: 18.3 Definitions

… ►In addition to the orthogonal property given by Table 18.3.1, the Chebyshev polynomials $T_n\left(x\right)$, $n=0,1,\mathrm{\dots },N$, are orthogonal on the discrete point set comprising the zeros $x_{N+1,n},n=1,2,\mathrm{\dots },N+1$, of $T_{N+1}\left(x\right)$: …

16: Bibliography I

… ►

An electrostatics model for zeros of general orthogonal polynomials. Pacific J. Math. 193 (2), pp. 355–369.

ⓘ

External Links:

ISSN 0030-8730, FullText, MathReview (T. Erber), ZentralBlatt

Referenced by:

§18.39(v).

Encodings:

BibTeX

►

More on electrostatic models for zeros of orthogonal polynomials. Numer. Funct. Anal. Optim. 21 (1-2), pp. 191–204.

ⓘ

External Links:

ISSN 0163-0563, FullText, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§18.39(v).

Encodings:

BibTeX

… ►

Bound on the extreme zeros of orthogonal polynomials. Proc. Amer. Math. Soc. 115 (1), pp. 131–140.

ⓘ

External Links:

ISSN 0002-9939, Document, MathReview (E. R. Love), ZentralBlatt

Referenced by:

(18.16.12), (18.16.13).

Encodings:

BibTeX

…

17: 18.36 Miscellaneous Polynomials

… ►EOP’s are non-classical in that not only are certain polynomial orders missing, but, also, not all EOP polynomial zeros are within the integration range of their generating measure, and EOP-orthogonality properties do not allow development of Gaussian-type quadratures. …

18: 28.34 Methods of Computation

… ►

Asymptotic approximations by zeros of orthogonal polynomials of increasing degree. See Volkmer (2008). This method also applies to eigenvalues of the Whittaker–Hill equation (§28.31(i)) and eigenvalues of Lamé functions (§29.3(i)).

…

19: Bibliography D

… ►

On the zeros of generalized Bessel polynomials. I. Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 1–13.

ⓘ

External Links:

ISSN 0019-3577, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§10.49(ii), §10.58.

Encodings:

BibTeX

►

On the zeros of generalized Bessel polynomials. II. Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 14–25.

ⓘ

External Links:

ISSN 0019-3577, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§10.49(ii), §10.58.

Encodings:

BibTeX

… ►

Zeros of Bernoulli, generalized Bernoulli and Euler polynomials. Mem. Amer. Math. Soc. 73 (386), pp. iv+94.

ⓘ

External Links:

ISSN 0065-9266, MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i), §24.12(iii), §24.16(ii).

Encodings:

BibTeX

… ►

On multiple zeros of Bernoulli polynomials. Acta Arith. 134 (2), pp. 149–155.

ⓘ

External Links:

ISSN 0065-1036, Document, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.12(iv).

Encodings:

BibTeX

►

Sharp bounds for the extreme zeros of classical orthogonal polynomials. J. Approx. Theory 162 (10), pp. 1793–1804.

ⓘ

External Links:

ISSN 0021-9045, Document, FullText, MathReview (Francisco Marcellán), ZentralBlatt

Referenced by:

(18.16.12), (18.16.13), §18.16(ii), §18.16(ii), §18.16(iv).

Encodings:

BibTeX

…

20: Bibliography V

… ►

Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials. J. Comput. Appl. Math. 213 (2), pp. 488–500.

ⓘ

External Links:

ISSN 0377-0427, Document, FullText, MathReview (Javier Segura), ZentralBlatt

Referenced by:

item (f), §28.34(ii), §29.20(i).

Encodings:

BibTeX

…