large degree

(0.001 seconds)

1—10 of 28 matching pages

1: 14.26 Uniform Asymptotic Expansions

§14.26 Uniform Asymptotic Expansions

…

2: Bibliography U

… ►

F. Ursell (1984) Integrals with a large parameter: Legendre functions of large degree and fixed order. Math. Proc. Cambridge Philos. Soc. 95 (2), pp. 367–380.

ⓘ

External Links:: ISSN 0305-0041, Document, MathReview (Roderick Wong), ZentralBlatt
Referenced by:: §14.26.
Encodings:: BibTeX

…

3: 14.15 Uniform Asymptotic Approximations

… ►

§14.15(iii) Large $\nu$ , Fixed $\mu$

… ►

4: Bibliography T

… ►

N. M. Temme (1986) Laguerre polynomials: Asymptotics for large degree. Technical report Technical Report AM-R8610, CWI, Amsterdam, The Netherlands.

ⓘ

External Links:: FullText
Referenced by:: §2.4(vi).
Encodings:: BibTeX

…

5: 14.20 Conical (or Mehler) Functions

… ►

§14.20(vii) Asymptotic Approximations: Large $\tau$ , Fixed $\mu$

… ►

§14.20(viii) Asymptotic Approximations: Large $\tau$ , $0\leq\mu\leq A\tau$

…

6: 18.40 Methods of Computation

… ►Usually, however, other methods are more efficient, especially the numerical solution of difference equations (§3.6) and the application of uniform asymptotic expansions (when available) for OP’s of large degree. …

7: Bibliography L

… ►

J. L. López and N. M. Temme (2010b) Large degree asymptotics of generalized Bernoulli and Euler polynomials. J. Math. Anal. Appl. 363 (1), pp. 197–208.

ⓘ

External Links:: ISSN 0022-247X, Document, Link, MathReview (Richard B. Paris), ZentralBlatt
Referenced by:: §24.16(i), §24.16(i).
Encodings:: BibTeX

…

8: 2.10 Sums and Sequences

… ►

Example

…

9: 18.26 Wilson Class: Continued

… ►For asymptotic expansions of Wilson polynomials of large degree see Wilson (1991), and for asymptotic approximations to their largest zeros see Chen and Ismail (1998). …

10: 18.2 General Orthogonal Polynomials

… ►If the polynomials

p_{n}(x)

(

n=0,1,\ldots,N

) are orthogonal on a finite set

X

N+1

distinct points as in (18.2.3), then the polynomial

p_{N+1}(x)

of degree

N+1

, up to a constant factor defined by (18.2.8) or (18.2.10), vanishes on

X

. … ►

Degree lowering and raising differentiation formulas and structure relations

►For a large class of OP’s

p_{n}

there exist pairs of differentiation formulas …If

A_{n}(x)

and

B_{n}(x)

are polynomials of degree independent of

n

, and moreover

\pi_{n}(x)

is a polynomial

\pi(x)

independent of

n

then … ►Polynomials

p_{n}(x)