rank of singularity

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11—14 of 14 matching pages

11: 13.14 Definitions and Basic Properties

… ►It has a regular singularity at the origin with indices $\frac{1}{2}\pm \mu$, and an irregular singularity at infinity of rank one. …

12: 10.2 Definitions

… ►This differential equation has a regular singularity at $z=0$ with indices $\pm \nu$, and an irregular singularity at $z=\mathrm{\infty }$ of rank $1$; compare §§2.7(i) and 2.7(ii). …

13: 10.47 Definitions and Basic Properties

… ►Equations (10.47.1) and (10.47.2) each have a regular singularity at $z=0$ with indices $n$, $-n-1$, and an irregular singularity at $z=\mathrm{\infty }$ of rank $1$; compare §§2.7(i)–2.7(ii). …

14: 15.17 Mathematical Applications

… ►First, as spherical functions on noncompact Riemannian symmetric spaces of rank one, but also as associated spherical functions, intertwining functions, matrix elements of SL$(2,ℝ)$, and spherical functions on certain nonsymmetric Gelfand pairs. … ►The three singular points in Riemann’s differential equation (15.11.1) lead to an interesting Riemann sheet structure. …