# Ince polynomials

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## 10 matching pages

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

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

… ►When $p$ is a nonnegative integer, the parameter $\eta $ can be chosen so that solutions of (28.31.3) are trigonometric polynomials, called*Ince polynomials*. They are denoted by … … ►The normalization is given by …

##### 2: 29.15 Fourier Series and Chebyshev Series

###### Polynomial ${\mathrm{\mathit{u}\mathit{E}}}_{2n}^{m}(z,{k}^{2})$

… ►###### Polynomial ${\mathrm{\mathit{s}\mathit{E}}}_{2n+1}^{m}(z,{k}^{2})$

… ►###### Polynomial ${\mathrm{\mathit{c}\mathit{E}}}_{2n+1}^{m}(z,{k}^{2})$

… ►###### Polynomial ${\mathrm{\mathit{d}\mathit{E}}}_{2n+1}^{m}(z,{k}^{2})$

… ►###### Polynomial ${\mathrm{\mathit{s}\mathit{c}\mathit{E}}}_{2n+2}^{m}(z,{k}^{2})$

…##### 3: 29.21 Tables

Ince (1940a) tabulates the eigenvalues ${a}_{\nu}^{m}\left({k}^{2}\right)$, ${b}_{\nu}^{m+1}\left({k}^{2}\right)$ (with ${a}_{\nu}^{2m+1}$ and ${b}_{\nu}^{2m+1}$ interchanged) for ${k}^{2}=0.1,0.5,0.9$, $\nu =-\frac{1}{2},0(1)25$, and $m=0,1,2,3$. Precision is 4D.

##### 4: 29.6 Fourier Series

##### 5: 29 Lamé Functions

##### 6: 29.1 Special Notation

##### 7: Bibliography I

##### 8: 29.17 Other Solutions

##### 9: 29.7 Asymptotic Expansions

##### 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.