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irregular singularities of rank 1

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1: 31.12 Confluent Forms of Heun’s Equation
This has regular singularities at z = 0 and 1 , and an irregular singularity of rank 1 at z = . … This has irregular singularities at z = 0 and , each of rank 1 . …
2: 30.2 Differential Equations
This equation has regular singularities at z = ± 1 with exponents ± 1 2 μ and an irregular singularity of rank 1 at z = (if γ 0 ). …
3: 2.7 Differential Equations
§2.7(ii) Irregular Singularities of Rank 1
The most common type of irregular singularity for special functions has rank 1 and is located at infinity. …
4: 2.9 Difference Equations
This situation is analogous to second-order homogeneous linear differential equations with an irregular singularity of rank 1 at infinity (§2.7(ii)). …
5: 33.2 Definitions and Basic Properties
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)). …
6: 33.14 Definitions and Basic Properties
Again, there is a regular singularity at r = 0 with indices + 1 and - , and an irregular singularity of rank 1 at r = . …
7: 10.2 Definitions
This differential equation has a regular singularity at z = 0 with indices ± ν , and an irregular singularity at z = of rank 1 ; compare §§2.7(i) and 2.7(ii). …
8: 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). …
9: 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.
  • 10: 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. …