# large degree

(0.001 seconds)

## 1—10 of 29 matching pages

##### 1: 14.26 Uniform Asymptotic Expansions

###### §14.26 Uniform Asymptotic Expansions

…##### 2: Bibliography U

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

##### 3: 14.15 Uniform Asymptotic Approximations

##### 4: Bibliography T

…
►
Laguerre polynomials: Asymptotics for large degree.
Technical report
Technical Report AM-R8610, CWI, Amsterdam, The Netherlands.
…

##### 5: 14.20 Conical (or Mehler) Functions

…
►

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

… ►###### §14.20(viii) Asymptotic Approximations: Large $\tau $, $0\le \mu \le 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

…
►
Large degree asymptotics of generalized Bernoulli and Euler polynomials.
J. Math. Anal. Appl. 363 (1), pp. 197–208.
…

##### 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 ${p}_{n}(x)$ ($n=0,1,\mathrm{\dots},N$) are orthogonal on a finite set $X$ of $N+1$ 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 ${p}_{n}(x)$ of degree $n$ ($n=0,1,2,\mathrm{\dots}$) are called*Sheffer polynomials*if they are generated by a generating function of the form …