About the Project
NIST

irregular singularity

AdvancedHelp

(0.001 seconds)

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 ρ = 0 with indices + 1 and - , and an irregular singularity of rank 1 at ρ = (§§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 + 1 and - , and an irregular singularity of rank 1 at r = . …
    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 = 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 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: 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. …
    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).