representation%20by%20squares
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4 matching pages
1: Bibliography M
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An integral representation for the Bessel form.
J. Comput. Appl. Math. 57 (1-2), pp. 251–260.
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An integral representation for the Lambert function.
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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions.
Ramanujan J. 6 (1), pp. 7–149.
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New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function.
Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.
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On the representation of numbers as a sum of
squares.
Quarterly Journal of Math. 48, pp. 93–104.
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2: 18.39 Applications in the Physical Sciences
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►where is the (squared) angular momentum operator (14.30.12).
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►with an infinite set of orthonormal eigenfunctions
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►The bound state eigenfunctions of the radial Coulomb Schrödinger operator are discussed in §§18.39(i) and 18.39(ii), and the -function normalized (non-) in Chapter 33, where the solutions appear as Whittaker functions.
…Here tridiagonal representations of simple Schrödinger operators play a similar role.
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►The fact that non- continuum scattering eigenstates may be expressed in terms or (infinite) sums of functions allows a reformulation of scattering theory in atomic physics wherein no non- functions need appear.
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3: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Tables of the Incomplete Gamma Function Ratio: The Chi-square Integral, the Poisson Distribution.
Justus von Liebig Verlag, Darmstadt (German, English).
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Closed-form representations of the Lambert function.
Fract. Calc. Appl. Anal. 7 (2), pp. 177–190.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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4: Bibliography S
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The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions.
2nd edition, Graduate Texts in Mathematics, Vol. 203, Springer-Verlag, New York.
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Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation.
Adv. Quantum Chem. 72, pp. 95–127.
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On integral representations for Lamé and other special functions.
SIAM J. Math. Anal. 11 (4), pp. 702–723.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Algorithm AS 239. Chi-squared and incomplete gamma integral.
Appl. Statist. 37 (3), pp. 466–473.
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