# Abel

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## 7 matching pages

##### 1: 22.18 Mathematical Applications

###### §22.18(iv) Elliptic Curves and the Jacobi–Abel Addition Theorem

… ►For any two points $({x}_{1},{y}_{1})$ and $({x}_{2},{y}_{2})$ on this curve, their*sum*$({x}_{3},{y}_{3})$, always a third point on the curve, is defined by the Jacobi–Abel addition law …a construction due to Abel; see Whittaker and Watson (1927, pp. 442, 496–497). …

##### 2: 1.15 Summability Methods

###### Abel Summability

… ►###### Abel Means

… ► $A(r,\theta )$ is a harmonic function in polar coordinates ((1.9.27)), and … ►Here $u(x,y)=A(r,\theta )$ is the*Abel*(or

*Poisson*)

*sum*of $f(\theta )$, and $v(x,y)$ has the series representation … ►

###### Abel Summability

…##### 3: 2.10 Sums and Sequences

*Abel–Plana formula*: … ►

The first infinite integral in (2.10.2) converges.

##### 4: 1.13 Differential Equations

*Abel’s identity*…

##### 5: 1.2 Elementary Algebra

###### §1.2(iv) Means

…##### 6: Bibliography B

##### 7: 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.