# irregular singularity

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## 11—19 of 19 matching pages

##### 11: Bibliography D

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Error bounds for exponentially improved asymptotic solutions of ordinary differential equations having irregular singularities of rank one.
Methods Appl. Anal. 3 (1), pp. 109–134.
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##### 12: 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)). …##### 13: 33.14 Definitions and Basic Properties

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###### §33.14(i) Coulomb Wave Equation

… ►Again, there is a regular singularity at $r=0$ with indices $\mathrm{\ell}+1$ and $-\mathrm{\ell}$, and an irregular singularity of rank 1 at $r=\mathrm{\infty}$. …##### 14: 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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##### 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: 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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##### 18: Bibliography E

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The Fuchsian equation of second order with four singularities.
Duke Math. J. 9 (1), pp. 48–58.
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Generalized Bernoulli numbers, generalized irregular primes, and class number.
Ann. Univ. Turku. Ser. A I 178, pp. 1–72.
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##### 19: Bibliography

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Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions.
J. Math. Physics 33, pp. 111–116.
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Unsteady lifting-line theory as a singular-perturbation problem.
J. Fluid Mech 153, pp. 59–81.
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Scattering by singular potentials with a perturbation – Theoretical introduction to Mathieu functions.
J. Mathematical Phys. 16, pp. 961–970.
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Singularities of Differentiable Maps. Vol. II.
Birkhäuser, Boston-Berlin.
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Normal forms of functions near degenerate critical points, the Weyl groups ${A}_{k},{D}_{k},{E}_{k}$ and Lagrangian singularities.
Funkcional. Anal. i Priložen. 6 (4), pp. 3–25 (Russian).
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