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31: 8.28 Software

… ►References to research software that is available in other ways is listed separately. …

32: 10.77 Software

… ►References to research software that is available in other ways is listed separately. …

33: 14.34 Software

… ►References to research software that is available in other ways is listed separately. …

34: 19.39 Software

… ►References to research software that is available in other ways is listed separately. …

35: 8.6 Integral Representations

… ►In (8.6.10)–(8.6.12), $c$ is a real constant and the path of integration is indented (if necessary) so that in the case of (8.6.10) it separates the poles of the gamma function from the pole at $s=a$, in the case of (8.6.11) it is to the right of all poles, and in the case of (8.6.12) it separates the poles of the gamma function from the poles at $s=0,1,2,\mathrm{\dots }$. …

36: 18.39 Applications in the Physical Sciences

… ►The solutions (18.39.8) are called the stationary states as separation of variables in (18.39.9) yields solutions of form … ►

§18.39(ii) A 3D Separable Quantum System, the Hydrogen Atom

… ►Since the operators $T_e+V(r)$ and ${\mathrm{L}}^2$ commute and have simultaneous eigenfunctions (see §1.3(iv)), the wave function $\mathrm{\Psi }(r,\theta ,\varphi )$ separates as …

37: 30.14 Wave Equation in Oblate Spheroidal Coordinates

… ►

§30.14(iv) Separation of Variables

… ►and $w_2$, $w_3$ satisfy (30.13.10) and (30.13.11), respectively, with ${\gamma }^2=-{\kappa }^2{c}^2\le 0$ and separation constants $\lambda$ and ${\mu }^2$. …

38: 30.13 Wave Equation in Prolate Spheroidal Coordinates

… ►

§30.13(iv) Separation of Variables

… ►with ${\gamma }^2={\kappa }^2{c}^2\ge 0$ and separation constants $\lambda$ and ${\mu }^2$. …

39: 25.10 Zeros

… ►Because $|Z(t)|=|\zeta \left(\frac{1}{2}+\mathrm{i}t\right)|$, $Z(t)$ vanishes at the zeros of $\zeta \left(\frac{1}{2}+\mathrm{i}t\right)$, which can be separated by observing sign changes of $Z(t)$. …

40: 12.5 Integral Representations

… ►where the contour separates the poles of $\mathrm{\Gamma }\left(t\right)$ from those of $\mathrm{\Gamma }\left(\frac{1}{2}+a-2t\right)$. … ►where the contour separates the poles of $\mathrm{\Gamma }\left(t\right)$ from those of $\mathrm{\Gamma }\left(\frac{1}{2}-a-2t\right)$. …