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11: 33.2 Definitions and Basic Properties
§33.2(i) Coulomb Wave Equation
This differential equation has a regular singularity at ρ = 0 with indices + 1 and - , and an irregular singularity of rank 1 at ρ = (§§2.7(i), 2.7(ii)). …
12: 14.2 Differential Equations
Equation (14.2.2) has regular singularities at x = 1 , - 1 , and , with exponent pairs { - 1 2 μ , 1 2 μ } , { - 1 2 μ , 1 2 μ } , and { ν + 1 , - ν } , respectively; compare §2.7(i). …
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: Bibliography B
  • W. G. C. Boyd and T. M. Dunster (1986) Uniform asymptotic solutions of a class of second-order linear differential equations having a turning point and a regular singularity, with an application to Legendre functions. SIAM J. Math. Anal. 17 (2), pp. 422–450.
  • 15: 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. …In effect, the regular singularities of the hypergeometric differential equation at b and coalesce into an irregular singularity at . …
    16: 28.2 Definitions and Basic Properties
    This equation has regular singularities at 0 and 1, both with exponents 0 and 1 2 , and an irregular singular point at . …
    17: 1.16 Distributions
    (If a distribution is not regular, it is called singular.) …
    18: 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. …
    19: 15.10 Hypergeometric Differential Equation
    It has regular singularities at z = 0 , 1 , , with corresponding exponent pairs { 0 , 1 - c } , { 0 , c - a - b } , { a , b } , respectively. …
    20: 31.14 General Fuchsian Equation
    The general second-order Fuchsian equation with N + 1 regular singularities at z = a j , j = 1 , 2 , , N , and at , is given by …