algebraic form
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11—20 of 32 matching pages
11: 21.7 Riemann Surfaces
12: 32.10 Special Function Solutions
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►The solution (32.10.34) is an essentially transcendental function of both constants of integration since with and does not admit an algebraic first integral of the form
, with a constant.
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13: Bibliography T
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Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves.
Trans. Amer. Math. Soc. 365 (12), pp. 6697–6729.
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14: 2.6 Distributional Methods
15: 23.20 Mathematical Applications
16: 19.14 Reduction of General Elliptic Integrals
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►Legendre (1825–1832) showed that every elliptic integral can be expressed in terms of the three integrals in (19.1.2) supplemented by algebraic, logarithmic, and trigonometric functions.
…It then improves the classical method by first applying Hermite reduction to (19.2.3) to arrive at integrands without multiple poles and uses implicit full partial-fraction decomposition and implicit root finding to minimize computing with algebraic extensions.
The choice among 21 transformations for final reduction to Legendre’s normal form depends on inequalities involving the limits of integration and the zeros of the cubic or quartic polynomial.
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17: 18.38 Mathematical Applications
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Zhedanov Algebra
… ►See Zhedanov (1991), Granovskiĭ et al. (1992, §3), Koornwinder (2007a, §2) and Terwilliger (2011). Similar algebras can be associated with all families of OP’s in the -Askey scheme and the Askey scheme. … ►Algebraic structures were built of which special representations involve Dunkl type operators. In the -case this algebraic structure is called the double affine Hecke algebra (DAHA), introduced by Cherednik. …18: Errata
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►The spectral theory of these operators, based on Sturm-Liouville and Liouville normal forms, distribution theory, is now discussed more completely, including linear algebra, matrices, matrices as linear operators, orthonormal expansions, Stieltjes integrals/measures, generating functions.
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19: 3.6 Linear Difference Equations
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►Let us assume the normalizing condition is of the form
, where is a constant, and then solve the following tridiagonal system of algebraic equations for the unknowns ; see §3.2(ii).
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20: Bruce R. Miller
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►While developing the supporting theories, he discovered a passion for symbolic computation and computer algebra.
…There, he carried out research in non-linear dynamics and celestial mechanics, developing a specialized computer algebra system for high-order Lie transformations.
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►He is the developer of the tools used to process the DLMF into both book and web forms.
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