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11: 13.2 Definitions and Basic Properties
This equation has a regular singularity at the origin with indices 0 and 1 - b , and an irregular singularity at infinity of rank one. …
12: 13.14 Definitions and Basic Properties
It has a regular singularity at the origin with indices 1 2 ± μ , and an irregular singularity at infinity of rank one. …
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 = 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 , ) , 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. …