reduced residue system

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21: 28.27 Addition Theorems

… ►Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. …

22: 16.24 Physical Applications

… ►The $\mathit{3}j$ symbols, or Clebsch–Gordan coefficients, play an important role in the decomposition of reducible representations of the rotation group into irreducible representations. …

23: 3.11 Approximation Techniques

… ►With $b_0=1$, the last $q$ equations give $b_1,\mathrm{\dots },b_q$ as the solution of a system of linear equations. … ►(3.11.29) is a system of $n+1$ linear equations for the coefficients $a_0,a_1,\mathrm{\dots },a_n$. … ►Then the system (3.11.33) is diagonal and hence well-conditioned. … ►In consequence we can solve the system … ►In consequence of this structure the number of operations can be reduced to $nm=n{\log }_{2}n$ operations. …

24: Bibliography D

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The principal frequencies of vibrating systems with elliptic boundaries. Quart. J. Mech. Appl. Math. 8 (3), pp. 361–372.

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External Links:

Document, MathReview (M. A. Hyman), ZentralBlatt

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3rd item.

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The KP equation with quasiperiodic initial data. Phys. D 123 (1-4), pp. 123–152.

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Notes:

Nonlinear waves and solitons in physical systems (Los Alamos, NM, 1997)

External Links:

ISSN 0167-2789, Document, MathReview (Pavel Krejčí), ZentralBlatt

Referenced by:

§21.9.

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Texas Instruments, Inc..

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Notes:

Symbolic and extended-precision numerical computing system.

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index.

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An Introduction to Chaotic Dynamical Systems. The Benjamin/Cummings Publishing Co. Inc., Menlo Park, CA.

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External Links:

ISBN 0-8053-1601-9, MathReview (Richard C. Churchill), ZentralBlatt

Referenced by:

§3.8(viii).

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Irreducibility of certain generalized Bernoulli polynomials belonging to quadratic residue class characters. J. Number Theory 25 (1), pp. 72–80.

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External Links:

ISSN 0022-314X, Document, MathReview (T. Metsänkylä)

Referenced by:

§24.12(iii).

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25: 29.19 Physical Applications

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§29.19(i) Lamé Functions

… ►Brack et al. (2001) shows that Lamé functions occur at bifurcations in chaotic Hamiltonian systems. …

26: 8.24 Physical Applications

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§8.24(i) Incomplete Gamma Functions

►The function $\gamma (a,x)$ appears in: discussions of power-law relaxation times in complex physical systems (Sornette (1998)); logarithmic oscillations in relaxation times for proteins (Metzler et al. (1999)); Gaussian orbitals and exponential (Slater) orbitals in quantum chemistry (Shavitt (1963), Shavitt and Karplus (1965)); population biology and ecological systems (Camacho et al. (2002)). …

27: Simon Ruijsenaars

… ►His main research interests cover integrable systems, special functions, analytic difference equations, classical and quantum mechanics, and the relations between these areas. …

28: Funding

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Systems Integration for Manufacturing Applications Program of the Engineering Laboratory (formerly Manufacturing Engineering Laboratory)

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29: 26.22 Software

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GAP (website). A system for computational discrete algebra.

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Magma (website). A computational algebra system.

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30: Bruce R. Miller

… ►There, he carried out research in non-linear dynamics and celestial mechanics, developing a specialized computer algebra system for high-order Lie transformations. … ►In particular, he developed the LaTeXML system used for converting the LaTeX source documents into XML and MathML from which the DLMF website is constructed. …