# regular singularity

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## 11—20 of 22 matching pages

##### 11: 33.2 Definitions and Basic Properties

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###### §33.2(i) Coulomb Wave Equation

… ►This differential equation has a regular singularity at $\rho =0$ with indices $\mathrm{\ell}+1$ and $-\mathrm{\ell}$, and an irregular singularity of rank 1 at $\rho =\mathrm{\infty}$ (§§2.7(i), 2.7(ii)). …##### 12: 14.2 Differential Equations

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►Equation (14.2.2) has regular singularities at $x=1$, $-1$, and $\mathrm{\infty}$, with exponent pairs $\{-\frac{1}{2}\mu ,\frac{1}{2}\mu \}$, $\{-\frac{1}{2}\mu ,\frac{1}{2}\mu \}$, and $\{\nu +1,-\nu \}$, respectively; compare §2.7(i).
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##### 13: 10.47 Definitions and Basic Properties

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►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).
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##### 14: Bibliography B

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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.
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##### 15: 13.2 Definitions and Basic Properties

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►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 $\mathrm{\infty}$ coalesce into an irregular singularity at $\mathrm{\infty}$.
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##### 16: 28.2 Definitions and Basic Properties

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►This equation has regular singularities at 0 and 1, both with exponents 0 and $\frac{1}{2}$, and an irregular singular point at $\mathrm{\infty}$.
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##### 17: 1.16 Distributions

##### 18: 13.14 Definitions and Basic Properties

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►It has a regular singularity at the origin with indices $\frac{1}{2}\pm \mu $, and an irregular singularity at infinity of rank one.
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##### 19: 15.10 Hypergeometric Differential Equation

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►It has regular singularities at $z=0,1,\mathrm{\infty}$, with corresponding exponent pairs $\{0,1-c\}$, $\{0,c-a-b\}$, $\{a,b\}$, respectively.
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##### 20: 31.14 General Fuchsian Equation

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►The general second-order

*Fuchsian equation*with $N+1$ regular singularities at $z={a}_{j}$, $j=1,2,\mathrm{\dots},N$, and at $\mathrm{\infty}$, is given by …