# irregular singularities of rank 1

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## 1—10 of 12 matching pages

##### 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 $z=\infty$. … This has irregular singularities at $z=0$ and $\infty$, each of rank $1$. …
##### 2: 30.2 Differential Equations
This equation has regular singularities at $z=\pm 1$ with exponents $\pm\frac{1}{2}\mu$ and an irregular singularity of rank 1 at $z=\infty$ (if $\gamma\neq 0$). …
##### 3: 2.7 Differential Equations
###### §2.7(ii) IrregularSingularities of Rank1
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 $\rho=0$ with indices $\ell+1$ and $-\ell$, and an irregular singularity of rank 1 at $\rho=\infty$ (§§2.7(i), 2.7(ii)). …
##### 6: 33.14 Definitions and Basic Properties
Again, there is a regular singularity at $r=0$ with indices $\ell+1$ and $-\ell$, and an irregular singularity of rank 1 at $r=\infty$. …
##### 7: 10.2 Definitions
This differential equation has a regular singularity at $z=0$ with indices $\pm\nu$, and an irregular singularity at $z=\infty$ 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 $z=\infty$ 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. …