# algebraic form

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##### 2: 31.8 Solutions via Quadratures
βΊFor $\mathbf{m}=(m_{0},0,0,0)$, these solutions reduce to Hermite’s solutions (Whittaker and Watson (1927, §23.7)) of the Lamé equation in its algebraic form. …
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##### 4: 28.2 Definitions and Basic Properties
βΊWith $\zeta={\sin}^{2}z$ we obtain the algebraic form of Mathieu’s equation βΊ
28.2.2 $\zeta(1-\zeta)w^{\prime\prime}+\tfrac{1}{2}\left(1-2\zeta)w^{\prime}+\tfrac{1}% {4}(a-2q(1-2\zeta)\right)w=0.$
βΊWith $\zeta=\cos z$ we obtain another algebraic form: …
##### 5: 28.20 Definitions and Basic Properties
βΊwith its algebraic form βΊ
28.20.2 ${(\zeta^{2}-1)w^{\prime\prime}+\zeta w^{\prime}+\left(4q\zeta^{2}-2q-a\right)w% =0},$ $\zeta=\cosh z$.
##### 6: 34.5 Basic Properties: $\mathit{6j}$ Symbol
βΊIf any lower argument in a $\mathit{6j}$ symbol is $0$, $\tfrac{1}{2}$, or $1$, then the $\mathit{6j}$ symbol has a simple algebraic form. …
##### 7: 34.3 Basic Properties: $\mathit{3j}$ Symbol
βΊWhen any one of $j_{1},j_{2},j_{3}$ is equal to $0,\tfrac{1}{2}$, or $1$, the $\mathit{3j}$ symbol has a simple algebraic form. …
##### 8: Bibliography B
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• W. S. Burnside and A. W. Panton (1960) The Theory of Equations: With an Introduction to the Theory of Binary Algebraic Forms. Dover Publications, New York.
• ##### 9: Bibliography H
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• J. H. Hubbard and B. B. Hubbard (2002) Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. 2nd edition, Prentice Hall Inc., Upper Saddle River, NJ.
• ##### 10: 22.18 Mathematical Applications
βΊAlgebraic curves of the form $y^{2}=P(x)$, where $P$ is a nonsingular polynomial of degree 3 or 4 (see McKean and Moll (1999, §1.10)), are elliptic curves, which are also considered in §23.20(ii). …