# separation constants

(0.002 seconds)

## 1—10 of 36 matching pages

##### 1: 28.32 Mathematical Applications
The separated solutions $V(\xi,\eta)=v(\xi)w(\eta)$ can be obtained from the modified Mathieu’s equation (28.20.1) for $v$ and from Mathieu’s equation (28.2.1) for $w$, where $a$ is the separation constant and $q=\tfrac{1}{4}c^{2}k^{2}$. … is separated in this system, each of the separated equations can be reduced to the Whittaker–Hill equation (28.31.1), in which $A,B$ are separation constants. …
##### 2: 31.10 Integral Equations and Representations
###### Kernel Functions
where $\sigma$ is a separation constant. …
31.10.19 $\mathcal{K}(u,v,w)=u^{1-\gamma}v^{1-\delta}w^{1-\epsilon}\mathscr{C}_{1-\gamma% }\left(u\sqrt{\sigma_{1}}\right)\*\mathscr{C}_{1-\delta}\left(v\sqrt{\sigma_{2% }}\right)\mathscr{C}_{1-\epsilon}\left(\mathrm{i}w\sqrt{\sigma_{1}+\sigma_{2}}% \right),$
where $\sigma_{1}$ and $\sigma_{2}$ are separation constants. … and $\sigma_{1}$ and $\sigma_{2}$ are separation constants. …
##### 3: 29.18 Mathematical Applications
29.18.7 $\frac{{\mathrm{d}}^{2}u_{3}}{{\mathrm{d}\gamma}^{2}}+(h-\nu(\nu+1)k^{2}{% \operatorname{sn}}^{2}\left(\gamma,k\right))u_{3}=0,$
with separation constants $h$ and $\nu$. …
##### 4: 30.14 Wave Equation in Oblate Spheroidal Coordinates
and $w_{2}$, $w_{3}$ satisfy (30.13.10) and (30.13.11), respectively, with $\gamma^{2}=-\kappa^{2}c^{2}\leq 0$ and separation constants $\lambda$ and $\mu^{2}$. …
##### 5: Bibliography S
• J. A. Stratton, P. M. Morse, L. J. Chu, and R. A. Hutner (1941) Elliptic Cylinder and Spheroidal Wave Functions, Including Tables of Separation Constants and Coefficients. John Wiley and Sons, Inc., New York.
• J. A. Stratton, P. M. Morse, L. J. Chu, J. D. C. Little, and F. J. Corbató (1956) Spheroidal Wave Functions: Including Tables of Separation Constants and Coefficients. Technology Press of M. I. T. and John Wiley & Sons, Inc., New York.
• ##### 6: 30.13 Wave Equation in Prolate Spheroidal Coordinates
with $\gamma^{2}=\kappa^{2}c^{2}\geq 0$ and separation constants $\lambda$ and $\mu^{2}$. …
##### 7: 33.22 Particle Scattering and Atomic and Molecular Spectra
With $e$ denoting here the elementary charge, the Coulomb potential between two point particles with charges $Z_{1}e,Z_{2}e$ and masses $m_{1},m_{2}$ separated by a distance $s$ is $V(s)=Z_{1}Z_{2}e^{2}/(4\pi\varepsilon_{0}s)=Z_{1}Z_{2}\alpha\hbar c/s$, where $Z_{j}$ are atomic numbers, $\varepsilon_{0}$ is the electric constant, $\alpha$ is the fine structure constant, and $\hbar$ is the reduced Planck’s constant. The reduced mass is $m=m_{1}m_{2}/(m_{1}+m_{2})$, and at energy of relative motion $E$ with relative orbital angular momentum $\ell\hbar$, the Schrödinger equation for the radial wave function $w(s)$ is given by
33.22.1 $\left(-\frac{\hbar^{2}}{2m}\left(\frac{{\mathrm{d}}^{2}}{{\mathrm{d}s}^{2}}-% \frac{\ell(\ell+1)}{s^{2}}\right)+\frac{Z_{1}Z_{2}\alpha\hbar c}{s}\right)w=Ew,$
##### 8: 12.5 Integral Representations
where the contour separates the poles of $\Gamma\left(t\right)$ from those of $\Gamma\left(\tfrac{1}{2}+a-2t\right)$. … where the contour separates the poles of $\Gamma\left(t\right)$ from those of $\Gamma\left(\tfrac{1}{2}-a-2t\right)$. …
##### 9: 15.6 Integral Representations
In (15.6.6) the integration contour separates the poles of $\Gamma\left(a+t\right)$ and $\Gamma\left(b+t\right)$ from those of $\Gamma\left(-t\right)$, and $(-z)^{t}$ has its principal value. In (15.6.7) the integration contour separates the poles of $\Gamma\left(a+t\right)$ and $\Gamma\left(b+t\right)$ from those of $\Gamma\left(c-a-b-t\right)$ and $\Gamma\left(-t\right)$, and $(1-z)^{t}$ has its principal value. …
##### 10: 13.4 Integral Representations
where the contour of integration separates the poles of $\Gamma\left(a+t\right)$ from those of $\Gamma\left(-t\right)$. … where the contour of integration separates the poles of $\Gamma\left(a+t\right)\Gamma\left(1+a-b+t\right)$ from those of $\Gamma\left(-t\right)$. …