general form

SearchAdvancedHelp

(0.002 seconds)

11—20 of 133 matching pages

11: 18.32 OP’s with Respect to Freud Weights

… ►Generalized Freud weights have the form …

12: 3.5 Quadrature

… ►Similar results hold for the trapezoidal rule in the form … ►If $f\in C^{2m+2}[a,b]$, then the remainder $E_n(f)$ in (3.5.2) can be expanded in the form … ►

Gauss–Laguerre Formula

… ►If $\alpha \ne 0$ this is called the generalized Gauss–Laguerre formula. … ►Integrals of the form …

13: Bibliography C

… ►

Asymptotics and closed form of a generalized incomplete gamma function. J. Comput. Appl. Math. 67 (2), pp. 371–379.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.16.

Encodings:

BibTeX

…

14: Guide to Searching the DLMF

… ►To recognize the math symbols and structures, and to accommodate equivalence between various notations and various forms of expression, the search system maps the math part of your queries into a different form. … ►Note that the first form may match other functions $K$ than the Bessel $K$ function, so if you are sure you want Bessel $K$, you might as well enter one of the other 3 forms. … ►DLMF search is generally case-insensitive except when it is important to be case-sensitive, as when two different special functions have the same standard names but one name has a lower-case initial and the other is has an upper-case initial, such as si and Si, gamma and Gamma. …

15: 22.4 Periods, Poles, and Zeros

… ►Again, one member of each congruent set of zeros appears in the second row; all others are generated by translations of the form $2mK+2n\mathrm{i}{K}^{\prime }$, where $m,n\in \mathbb{Z}$. …

16: 18.2 General Orthogonal Polynomials

… ►If polynomials $p_n(x)$ are generated by recurrence relation (18.2.8) under assumption of inequality (18.2.9_5) (or similarly for the other three forms) then the $p_n(x)$ are orthogonal by Favard’s theorem, see §18.2(viii), in that the existence of a bounded non-decreasing function $\alpha (x)$ on $(a,b)$ yielding the orthogonality realtion (18.2.4_5) is guaranteed. … ►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 …

17: 21.7 Riemann Surfaces

… ►Then the prime form on the corresponding compact Riemann surface $\mathrm{\Gamma }$ is defined by … ►Generalizations of this identity are given in Fay (1973, Chapter 2). Fay derives (21.7.10) as a special case of a more general class of addition theorems for Riemann theta functions on Riemann surfaces. … ►These are Riemann surfaces that may be obtained from algebraic curves of the form …

18: 32.2 Differential Equations

… ►For arbitrary values of the parameters $\alpha$, $\beta$, $\gamma$, and $\delta$, the general solutions of ${\text{P}}_{\text{I}}$–${\text{P}}_{\text{VI}}$ are transcendental, that is, they cannot be expressed in closed-form elementary functions. …

19: 23.15 Definitions

… ►

§23.15(i) General Modular Functions

… ►The set of all bilinear transformations of this form is denoted by SL$(2,\mathbb{Z})$ (Serre (1973, p. 77)). … ►If, as a function of $q$, $f(\tau )$ is analytic at $q=0$, then $f(\tau )$ is called a modular form. If, in addition, $f(\tau )\to 0$ as $q\to 0$, then $f(\tau )$ is called a cusp form. …

20: 9.13 Generalized Airy Functions

§9.13 Generalized Airy Functions

►

§9.13(i) Generalizations from the Differential Equation

►Equations of the form … ► … ►