# Ince equation

(0.001 seconds)

## 1—10 of 17 matching pages

##### 1: 28.31 Equations of Whittaker–Hill and Ince

###### §28.31 Equations of Whittaker–Hill and Ince

… ►###### §28.31(ii) Equation of Ince; Ince Polynomials

… ►The result is the*Equation of Ince*: … ►

##### 2: 28.5 Second Solutions ${\mathrm{fe}}_{n}$, ${\mathrm{ge}}_{n}$

###### §28.5(i) Definitions

…##### 3: Bibliography I

##### 4: 28.2 Definitions and Basic Properties

##### 5: 31.14 General Fuchsian Equation

###### §31.14 General Fuchsian Equation

►###### §31.14(i) Definitions

… ►Heun’s equation (31.2.1) corresponds to $N=3$. ►###### Normal Form

… ►An algorithm given in Kovacic (1986) determines if a given (not necessarily Fuchsian) second-order homogeneous linear differential equation with rational coefficients has solutions expressible in finite terms (Liouvillean solutions). …##### 6: 1.13 Differential Equations

##### 7: 32.2 Differential Equations

###### §32.2 Differential Equations

►###### §32.2(i) Introduction

►The six Painlevé equations ${\text{P}}_{\text{I}}$–${\text{P}}_{\text{VI}}$ are as follows: … ►###### §32.2(ii) Renormalizations

… ► …##### 8: 31.12 Confluent Forms of Heun’s Equation

###### Confluent Heun Equation

… ►###### Doubly-Confluent Heun Equation

… ►###### Biconfluent Heun Equation

… ►###### Triconfluent Heun Equation

… ►##### 9: 29.3 Definitions and Basic Properties

##### 10: Errata

In Equation (1.13.4), the determinant form of the two-argument Wronskian

was added as an equality. In ¶Wronskian (in §1.13(i)), immediately below Equation (1.13.4), a sentence was added indicating that in general the $n$-argument Wronskian is given by $\mathcal{W}\left\{{w}_{1}(z),\mathrm{\dots},{w}_{n}(z)\right\}=det\left[{w}_{k}^{(j-1)}(z)\right]$, where $1\le j,k\le n$. Immediately below Equation (1.13.4), a sentence was added giving the definition of the $n$-argument Wronskian. It is explained just above (1.13.5) that this equation is often referred to as Abel’s identity. Immediately below Equation (1.13.5), a sentence was added explaining how it generalizes for $n$th-order differential equations. A reference to Ince (1926, §5.2) was added.