Abel summability

(0.001 seconds)

11—11 of 11 matching pages

11: Errata

… ►

Section 1.13

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

1.13.4

\mathscr{W}\left\{w_{1}(z),w_{2}(z)\right\}=\det\begin{bmatrix}w_{1}(z)&w_{2}(% z)\\ w_{1}^{\prime}(z)&w_{2}^{\prime}(z)\end{bmatrix}=w_{1}(z)w_{2}^{\prime}(z)-w_{% 2}(z)w_{1}^{\prime}(z)

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 $\mathscr{W}\left\{w_{1}(z),\ldots,w_{n}(z)\right\}=\det\left[w_{k}^{(j-1)}(z)\right]$ , where $1\leq j,k\leq n$ . 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.

…