# Theorem of Ince

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## 3 matching pages

##### 1: 28.5 Second Solutions ${\mathrm{fe}}_{n}$, ${\mathrm{ge}}_{n}$

##### 2: 28.2 Definitions and Basic Properties

##### 3: Errata

The largest known prime, which is a Mersenne prime, was updated from ${2}^{43,112,609}-1$ (2009) to ${2}^{82,589,933}-1$ (2018).

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.