# large degree

(0.001 seconds)

## 1—10 of 29 matching pages

##### 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.
##### 4: Bibliography T
• N. M. Temme (1986) Laguerre polynomials: Asymptotics for large degree. Technical report Technical Report AM-R8610, CWI, Amsterdam, The Netherlands.
##### 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.
##### 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 $X$ 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 $n$ ($n=0,1,2,\ldots$) are called Sheffer polynomials if they are generated by a generating function of the form …