# regular singularity

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## 11—20 of 22 matching pages

##### 11: 33.2 Definitions and Basic Properties
###### §33.2(i) Coulomb Wave Equation
This differential equation has a regular singularity at $\rho=0$ with indices $\ell+1$ and $-\ell$, and an irregular singularity of rank 1 at $\rho=\infty$ (§§2.7(i), 2.7(ii)). …
##### 12: 14.2 Differential Equations
Equation (14.2.2) has regular singularities at $x=1$, $-1$, and $\infty$, with exponent pairs $\left\{-\frac{1}{2}\mu,\frac{1}{2}\mu\right\}$, $\left\{-\frac{1}{2}\mu,\frac{1}{2}\mu\right\}$, and $\left\{\nu+1,-\nu\right\}$, 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 $z=\infty$ 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 $\infty$ coalesce into an irregular singularity at $\infty$. …
##### 16: 28.2 Definitions and Basic Properties
This equation has regular singularities at 0 and 1, both with exponents 0 and $\frac{1}{2}$, and an irregular singular point at $\infty$. …
##### 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 $\tfrac{1}{2}\pm\mu$, and an irregular singularity at infinity of rank one. …
##### 19: 15.10 Hypergeometric Differential Equation
It has regular singularities at $z=0,1,\infty$, 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 $z=a_{j}$, $j=1,2,\dots,N$, and at $\infty$, is given by …