zeng%C5%91%E2%80%93Askey%20polynomials

SearchAdvancedHelp

(0.002 seconds)

11—20 of 342 matching pages

11: 27.2 Functions

… ►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes. … ►

Table 27.2.1: Primes.

► ►►

$n$	$p_n$	$p_{n+10}$	$p_{n+20}$	$p_{n+30}$	$p_{n+40}$	$p_{n+50}$	$p_{n+60}$	$p_{n+70}$	$p_{n+80}$	$p_{n+90}$
…

►

►

Table 27.2.2: Functions related to division.

► ►►►►►

$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$
…
7	6	2	8	20	8	6	42	33	20	4	48	46	22	4	72
…
10	4	4	18	23	22	2	24	36	12	9	91	49	42	3	57
11	10	2	12	24	8	8	60	37	36	2	38	50	20	6	93
…

►

12: 18.13 Continued Fractions

§18.13 Continued Fractions

… ►

Legendre

… ►

Laguerre

… ►

Hermite

… ►See also Cuyt et al. (2008, pp. 91–99).

13: Bibliography N

… ►

On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

Referenced by:

§28.26(ii).

Encodings:

BibTeX

… ►

Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

ⓘ

External Links:

FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§19.37(iv).

Encodings:

BibTeX

… ►

On the large argument asymptotics of the Lommel function via Stieltjes transforms. Asymptot. Anal. 91 (3-4), pp. 265–281.

ⓘ

External Links:

ISSN 0921-7134, Document, MathReview Entry, ZentralBlatt

Referenced by:

§11.6(iii), §11.6(iii), §11.9(iii), §11.9(iii).

Encodings:

BibTeX

… ►

On the calculation of elliptic integrals of the second and third kinds. Zastos. Mat. 11, pp. 91–94.

ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

§19.36(ii).

Encodings:

BibTeX

… ►

Askey-Wilson polynomials: an affine Hecke algebra approach. In Laredo Lectures on Orthogonal Polynomials and Special Functions, Adv. Theory Spec. Funct. Orthogonal Polynomials, pp. 111–144.

ⓘ

External Links:

MathReview (V. L. Deshpande), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX

…

14: 24.2 Definitions and Generating Functions

… ►

§24.2(i) Bernoulli Numbers and Polynomials

… ►

§24.2(ii) Euler Numbers and Polynomials

… ►

${(-1)}^n{E}_{2n}>0$ .

… ►

Table 24.2.2: Bernoulli and Euler polynomials.

► ►►

$n$	$B_n\left(x\right)$	$E_n\left(x\right)$
…

►

…

15: Bibliography R

… ►

A non-negative representation of the linearization coefficients of the product of Jacobi polynomials. Canad. J. Math. 33 (4), pp. 915–928.

ⓘ

External Links:

ISSN 0008-414X, Document, Link, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.18(v).

Encodings:

BibTeX

… ►

On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

ⓘ

External Links:

ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

Encodings:

BibTeX

… ►

Uniform asymptotic approximations to the solutions of the Orr-Sommerfeld equation. I. Plane Couette flow. Studies in Appl. Math. 53, pp. 91–110.

ⓘ

External Links:

MathReview (T. W. Kao), ZentralBlatt

Referenced by:

§2.8(iii).

Encodings:

BibTeX

… ►

Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (4), pp. 91.

ⓘ

External Links:

ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

Encodings:

BibTeX

… ►

The umbral calculus. Pure and Applied Mathematics, Vol. 111, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York.

ⓘ

External Links:

ISBN 0-12-594380-6, MathReview (R. Askey)

Referenced by:

§18.2(xii).

Encodings:

BibTeX

…

16: Bibliography P

… ►

Zonal Polynomials of Order $1$ Through $12$ . In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (Eds.), Vol. 2, pp. 199–388.

ⓘ

External Links:

MathReview

Referenced by:

§35.11.

Encodings:

BibTeX

… ►

Orthogonal polynomials and some $q$-beta integrals of Ramanujan. J. Math. Anal. Appl. 112 (2), pp. 517–540.

ⓘ

External Links:

ISSN 0022-247X, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§18.33(iv), §18.33(v).

Encodings:

BibTeX

… ►

Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

ⓘ

Notes:

Double-precision Fortran, maximum accuracy 20S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

Encodings:

BibTeX

… ►

Primzahlverteilung. Die Grundlehren der mathematischen Wissenschaften, Vol. 91, Springer-Verlag, Berlin-Göttingen-Heidelberg (German).

ⓘ

Notes:

Reprinted in 1978.

External Links:

MathReview (A. E. Ingham), ZentralBlatt

Referenced by:

§27.11.

Encodings:

BibTeX

… ►

Stacking models of vesicles and compact clusters. J. Statist. Phys. 80 (3–4), pp. 755–779.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§8.24(ii).

Encodings:

BibTeX

…

17: Bibliography L

… ►

Elliptic Functions and Applications. Applied Mathematical Sciences, Vol. 80, Springer-Verlag, New York.

ⓘ

External Links:

ISBN 0-387-96965-9, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§19.2(ii), §19.36(iii), §20.13, §20.15, §20.2(i), §20.2(ii), §20.2(iii), §20.2(iv), §20.4(i), §20.5(i), §20.5(ii), §20.7(i), §20.7(ii), §20.7(iv), §20.7(vi), §20.7(vii), §20.7(vii), §20.7(viii), Ch.20, §22.10(i), §22.10(ii), §22.12, §22.13(i), §22.14(i), §22.14(ii), §22.14(iii), §22.14(iii), §22.15(i), §22.15(ii), §22.15(ii), §22.16(ii), §22.16(iii), §22.17(i), §22.18(i), §22.18(iii), §22.19(ii), §22.19(i), §22.19(i), §22.19(ii), §22.19(ii), §22.19(iv), §22.19(v), §22.2, §22.20(vii), §22.21, §22.4(i), §22.4(iii), §22.5(i), §22.5(ii), §22.6(ii), §22.6(iii), §22.6(iv), §22.7(i), §22.7(ii), §22.8(i), §22.8(ii), Ch.22, §23.10(i), §23.10(i), §23.10(iii), §23.10(iv), §23.12, §23.2(ii), §23.2(iii), §23.2(iii), §23.21(i), §23.3(i), §23.3(ii), §23.6(iv), §23.6(i), §23.6(i), §23.6(ii), §23.6(ii), §23.6(iii), §23.7, §23.8(i), §23.8(ii), §23.8(iii), Ch.23.

Encodings:

BibTeX

►

Algorithm 917: complex double-precision evaluation of the Wright $\omega$ function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

ⓘ

External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§4.13, 2nd item, §4.48(iv).

Encodings:

BibTeX

… ►

An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

ⓘ

External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.11.

Encodings:

BibTeX

… ►

Asymptotic expansions of the Whittaker functions for large order parameter. Methods Appl. Anal. 6 (2), pp. 249–256.

ⓘ

Notes:

Dedicated to Richard A. Askey on the occasion of his 65th birthday, Part II

External Links:

ISSN 1073-2772, Pdf, MathReview, ZentralBlatt

Referenced by:

§13.21(i), §13.24(ii).

Encodings:

BibTeX

… ►

Monotonicity of the differences of zeros of Bessel functions as a function of order. Proc. Amer. Math. Soc. 15 (1), pp. 91–96.

ⓘ

External Links:

ISSN 0002-9939, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§10.21(ii).

Encodings:

BibTeX

…

18: Bibliography K

… ►

A proof of the $q$-Macdonald-Morris conjecture for $B{C}_n$ . Mem. Amer. Math. Soc. 108 (516), pp. vi+80.

ⓘ

External Links:

ISSN 0065-9266, MathReview (Eric M. Opdam), ZentralBlatt

Referenced by:

§17.14.

Encodings:

BibTeX

… ►

Linear convergence and the bisection algorithm. Amer. Math. Monthly 93 (1), pp. 48–51.

ⓘ

External Links:

ISSN 0002-9890, FullText, MathReview (J. G. Herriot), ZentralBlatt

Referenced by:

§3.8(iii).

Encodings:

BibTeX

… ►

The structure relation for Askey-Wilson polynomials. J. Comput. Appl. Math. 207 (2), pp. 214–226.

ⓘ

External Links:

ISSN 0377-0427, Document, Link, MathReview Entry

Referenced by:

(18.9.18_5).

Encodings:

BibTeX

►

The Askey scheme as a four-manifold with corners. Ramanujan J. 20 (3), pp. 409–439.

ⓘ

External Links:

ISSN 1382-4090, Document, FullText, MathReview (José Luis López), ZentralBlatt

Referenced by:

§18.26(v), §18.26(v).

Encodings:

BibTeX

►

Askey-Wilson polynomial. Scholarpedia 7 (7), pp. 7761.

ⓘ

Notes:

Electronic only

External Links:

Document, FullText

Referenced by:

§18.28(i), §18.28(i).

Encodings:

BibTeX

…

19: Bibliography C

… ►

Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams. J. Comput. Appl. Math. 115 (1-2), pp. 93–99.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Lorenzo L. Salcedo), ZentralBlatt

Referenced by:

§16.24(ii).

Encodings:

BibTeX

… ►

Work Group of Computational Mathematics, University of Kassel, Germany.

ⓘ

Notes:

Computer Algebra and Orthogonal Polynomials: a Web service using Maple for online generation of formulas and graphs of orthogonal polynomials belonging to the Askey scheme. For further information see Swarttouw (1997) and Koepf (1999).

External Links:

CAOP

Referenced by:

1st item.

Encodings:

BibTeX

… ►

On the zeros of the Askey-Wilson polynomials, with applications to coding theory. SIAM J. Math. Anal. 18 (1), pp. 191–207.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX

… ►

Über die Fälle, wenn die Reihe von der Form $y=1+\frac{\alpha }{1}\cdot \frac{\beta }{\gamma }x+\frac{\alpha \cdot \alpha +1}{1\cdot 2}\cdot \frac{\beta \cdot \beta +1}{\gamma \cdot \gamma +1}{x}^2+$ etc. ein Quadrat von der Form $z=1+\frac{{\alpha }^{\prime }}{1}\cdot \frac{{\beta }^{\prime }}{{\gamma }^{\prime }}\cdot \frac{{\delta }^{\prime }}{{ϵ}^{\prime }}x+\frac{{\alpha }^{\prime }\cdot {\alpha }^{\prime }+1}{1\cdot 2}\cdot \frac{{\beta }^{\prime }\cdot {\beta }^{\prime }+1}{{\gamma }^{\prime }\cdot {\gamma }^{\prime }+1}\cdot \frac{{\delta }^{\prime }\cdot {\delta }^{\prime }+1}{{ϵ}^{\prime }\cdot {ϵ}^{\prime }+1}{x}^2+$ etc. hat. J. Reine Angew. Math. 3, pp. 89–91.

ⓘ

External Links:

Link, MathReview Entry, ZentralBlatt

Referenced by:

§16.12.

Encodings:

BibTeX

… ►

Inverse Acoustic and Electromagnetic Scattering Theory. 2nd edition, Applied Mathematical Sciences, Vol. 93, Springer-Verlag, Berlin.

ⓘ

External Links:

ISBN 3-540-62838-X, MathReview, ZentralBlatt

Referenced by:

§10.73(i).

Encodings:

BibTeX

…

20: 3.9 Acceleration of Convergence

… ►

Table 3.9.1: Shanks’ transformation for $s_n={\sum }_{j=1}^n{(-1)}^{j+1}{j}^{-2}$.

► ►►►►

$n$	$t_{n,2}$	$t_{n,4}$	$t_{n,6}$	$t_{n,8}$	$t_{n,10}$
…
4	0.82221 76684 88	0.82246 28314 41	0.82246 69467 93	0.82246 70314 36	0.82246 70333 75
…
9	0.82248 70624 89	0.82246 71865 91	0.82246 70351 34	0.82246 70334 48	0.82246 70334 24
…

►

…