# irregular singularity

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## 11—19 of 19 matching pages

##### 11: Bibliography D
• T. M. Dunster (1996c) 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.
• ##### 12: 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)). …
##### 13: 33.14 Definitions and Basic Properties
###### §33.14(i) Coulomb Wave Equation
Again, there is a regular singularity at $r=0$ with indices $\ell+1$ and $-\ell$, and an irregular singularity of rank 1 at $r=\infty$. …
##### 14: 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). …
##### 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: 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. …
##### 18: Bibliography E
• A. Erdélyi (1942b) The Fuchsian equation of second order with four singularities. Duke Math. J. 9 (1), pp. 48–58.
• R. Ernvall (1979) Generalized Bernoulli numbers, generalized irregular primes, and class number. Ann. Univ. Turku. Ser. A I 178, pp. 1–72.
• ##### 19: Bibliography
• M. Abramowitz (1954) Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions. J. Math. Physics 33, pp. 111–116.
• A. R. Ahmadi and S. E. Widnall (1985) Unsteady lifting-line theory as a singular-perturbation problem. J. Fluid Mech 153, pp. 59–81.
• H. H. Aly, H. J. W. Müller-Kirsten, and N. Vahedi-Faridi (1975) Scattering by singular potentials with a perturbation – Theoretical introduction to Mathieu functions. J. Mathematical Phys. 16, pp. 961–970.
• V. I. Arnol’d, S. M. Guseĭn-Zade, and A. N. Varchenko (1988) Singularities of Differentiable Maps. Vol. II. Birkhäuser, Boston-Berlin.
• V. I. Arnol’d (1972) 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).