separation constant

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11: 13.4 Integral Representations

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

12: 16.5 Integral Representations and Integrals

… ►where the contour of integration separates the poles of $\mathrm{\Gamma }\left(a_k+s\right)$, $k=1,\mathrm{\dots },p$, from those of $\mathrm{\Gamma }\left(-s\right)$. …

13: 28.33 Physical Applications

… ►where $q=\frac{1}{4}{c}^2{k}^2$ and $a_n(q)$ or $b_n(q)$ is the separation constant; compare (28.12.11), (28.20.11), and (28.20.12). …

14: 10.32 Integral Representations

… ►In (10.32.14) the integration contour separates the poles of $\mathrm{\Gamma }\left(t\right)$ from the poles of $\mathrm{\Gamma }\left(\frac{1}{2}-t-\nu \right)\mathrm{\Gamma }\left(\frac{1}{2}-t+\nu \right)$. …

15: 16.17 Definition

… ►where the integration path $L$ separates the poles of the factors $\mathrm{\Gamma }\left(b_{\mathrm{\ell }}-s\right)$ from those of the factors $\mathrm{\Gamma }\left(1-a_{\mathrm{\ell }}+s\right)$. …

16: 9.12 Scorer Functions

… ►where the integration contour separates the poles of $\mathrm{\Gamma }\left(\frac{1}{3}+\frac{1}{3}t\right)$ from those of $\mathrm{\Gamma }\left(-t\right)$. …

17: Bibliography K

… ►

Separation of Variables for Riemannian Spaces of Constant Curvature. Longman Scientific & Technical, Harlow.

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External Links:

ISBN 0-582-98807-1, MathReview (H. Kilp), ZentralBlatt

Referenced by:

§31.17(i).

Encodings:

BibTeX

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18: 10.9 Integral Representations

… ►where the path of integration separates the poles of $\mathrm{\Gamma }\left(-t\right)$ from those of $\mathrm{\Gamma }\left(2t+\mu +\nu +1\right)$. …

19: Bibliography O

… ►

Triorthogonal systems in spaces of constant curvature in which the equation ${\mathrm{\Delta }}_{2}u+\lambda u=0$ allows a complete separation of variables. Mat. Sbornik N.S. 27(69) (3), pp. 379–426 (Russian).

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Notes:

In Russian.

External Links:

MathReview (H. Busemann), ZentralBlatt

Referenced by:

§31.17(i).

Encodings:

BibTeX

…

20: 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 $s=0,1,2,\mathrm{\dots }$. …