# normalizing factor

(0.002 seconds)

## 1—10 of 14 matching pages

##### 1: 3.6 Linear Difference Equations
It therefore remains to apply a normalizing factor $\Lambda$. … The normalizing factor $\Lambda$ can be the true value of $w_{0}$ divided by its trial value, or $\Lambda$ can be chosen to satisfy a known property of the wanted solution of the form … …
##### 2: 3.7 Ordinary Differential Equations
The eigenvalues $\lambda_{k}$ are simple, that is, there is only one corresponding eigenfunction (apart from a normalization factor), and when ordered increasingly the eigenvalues satisfy …
##### 3: 18.2 General Orthogonal Polynomials
The orthogonality relations (18.2.1)–(18.2.3) each determine the polynomials $p_{n}(x)$ uniquely up to constant factors, which may be fixed by suitable normalization. …
##### 4: 28.5 Second Solutions $\mathrm{fe}_{n}$, $\mathrm{ge}_{n}$
The factors $C_{n}(q)$ and $S_{n}(q)$ in (28.5.1) and (28.5.2) are normalized so that
28.5.5 $(C_{n}(q))^{2}\int_{0}^{2\pi}(f_{n}(x,q))^{2}\mathrm{d}x=(S_{n}(q))^{2}\int_{0% }^{2\pi}(g_{n}(x,q))^{2}\mathrm{d}x=\pi.$
##### 6: Bibliography C
• B. C. Carlson and J. FitzSimons (2000) Reduction theorems for elliptic integrands with the square root of two quadratic factors. J. Comput. Appl. Math. 118 (1-2), pp. 71–85.
• B. C. Carlson (1964) Normal elliptic integrals of the first and second kinds. Duke Math. J. 31 (3), pp. 405–419.
• D. C. Cronemeyer (1991) Demagnetization factors for general ellipsoids. J. Appl. Phys. 70 (6), pp. 2911–2914.
• Cunningham Project (website)
• S. W. Cunningham (1969) Algorithm AS 24: From normal integral to deviate. Appl. Statist. 18 (3), pp. 290–293.
• ##### 7: 19.16 Definitions
19.16.1 $R_{F}\left(x,y,z\right)=\frac{1}{2}\int_{0}^{\infty}\frac{\mathrm{d}t}{s(t)},$
19.16.2 $R_{J}\left(x,y,z,p\right)=\frac{3}{2}\int_{0}^{\infty}\frac{\mathrm{d}t}{s(t)(% t+p)},$
19.16.2_5 $R_{G}\left(x,y,z\right)=\frac{1}{4}\int_{0}^{\infty}\frac{1}{s(t)}\*\left(% \frac{x}{t+x}+\frac{y}{t+y}+\frac{z}{t+z}\right)t\mathrm{d}t.$
19.16.4 $s(t)=\sqrt{t+x}\sqrt{t+y}\sqrt{t+z}.$
It should be noted that the integrals (19.16.1)–(19.16.2_5) have been normalized so that $R_{F}\left(1,1,1\right)=R_{J}\left(1,1,1,1\right)=R_{G}\left(1,1,1\right)=1$. …
##### 8: 28.12 Definitions and Basic Properties
In consequence, for the Floquet solutions $w(z)$ the factor $e^{\pi\mathrm{i}\nu}$ in (28.2.14) is no longer $\pm 1$. …
28.12.2 $\lambda_{\nu}\left(-q\right)=\lambda_{\nu}\left(q\right)=\lambda_{-\nu}\left(q% \right).$
As in §28.7 values of $q$ for which (28.2.16) has simple roots $\lambda$ are called normal values with respect to $\nu$. For real values of $\nu$ and $q$ all the $\lambda_{\nu}\left(q\right)$ are real, and $q$ is normal. … If $q$ is a normal value of the corresponding equation (28.2.16), then these functions are uniquely determined as analytic functions of $z$ and $q$ by the normalization
##### 9: 10.22 Integrals
10.22.72 $\int_{0}^{\infty}J_{\mu}\left(at\right)J_{\nu}\left(bt\right)J_{\nu}\left(ct% \right)t^{1-\mu}\mathrm{d}t=\frac{(bc)^{\mu-1}\sin\left((\mu-\nu)\pi\right)(% \sinh\chi)^{\mu-\frac{1}{2}}}{(\frac{1}{2}\pi^{3})^{\frac{1}{2}}a^{\mu}}{% \mathrm{e}}^{(\mu-\frac{1}{2})\mathrm{i}\pi}Q^{\frac{1}{2}-\mu}_{\nu-\frac{1}{% 2}}\left(\cosh\chi\right),$ $\Re\mu>-\tfrac{1}{2},\Re\nu>-1,a>b+c,\cosh\chi=(a^{2}-b^{2}-c^{2})/(2bc)$.
##### 10: Bibliography
• A. G. Adams (1969) Algorithm 39: Areas under the normal curve. The Computer Journal 12 (2), pp. 197–198.
• A. Adelberg (1992) On the degrees of irreducible factors of higher order Bernoulli polynomials. Acta Arith. 62 (4), pp. 329–342.
• V. I. Arnol’d (1972) Normal forms of functions near degenerate critical points, the Weyl groups ${A}_{k},{D}_{k},{E}_{k}$ and Lagrangian singularities. Funkcional. Anal. i Priložen. 6 (4), pp. 3–25 (Russian).
• V. I. Arnol’d (1974) Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).
• V. I. Arnol’d (1975) Critical points of smooth functions, and their normal forms. Uspehi Mat. Nauk 30 (5(185)), pp. 3–65 (Russian).