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1: 26.13 Permutations: Cycle Notation

… ►An explicit representation of $\sigma$ can be given by the $2\times n$ matrix: …

2: 14.30 Spherical and Spheroidal Harmonics

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Explicit Representation

… ►For a series representation of the product of two Dirac deltas in terms of products of spherical harmonics see §1.17(iii). …

3: 18.5 Explicit Representations

§18.5 Explicit Representations

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Chebyshev

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$T_5\left(x\right)=16x^5-20x^3+5x,$

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$L_6\left(x\right)=\frac{1}{720}{x}^6-\frac{1}{20}{x}^5+\frac{5}{8}{x}^4-\frac{10}{3}{x}^3+\frac{15}{2}{x}^2-6x+1.$

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4: Bibliography G

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Integral representations for computing real parabolic cylinder functions. Numer. Math. 98 (1), pp. 105–134.

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External Links:

ISSN 0029-599X, Document, MathReview Entry, ZentralBlatt

Referenced by:

§12.18.

Encodings:

BibTeX

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

External Links:

ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, §10.77(ix).

Encodings:

BibTeX

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Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.

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External Links:

FullText, MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§26.1, §26.1, Notations S, Notations S.

Encodings:

BibTeX

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Explicit formulas for Bernoulli numbers. Amer. Math. Monthly 79, pp. 44–51.

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External Links:

FullText, MathReview (B. M. Stewart), ZentralBlatt

Referenced by:

§24.15(iii), §24.6.

Encodings:

BibTeX

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Representations of Integers as Sums of Squares. Springer-Verlag, New York.

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External Links:

ISBN 0-387-96126-7, MathReview (Harvey Cohn), ZentralBlatt

Referenced by:

§27.13(iv).

Encodings:

BibTeX

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5: 18.39 Applications in the Physical Sciences

… ►Here are three examples of solutions for (18.39.8) for explicit choices of $V(x)$ and with the ${\psi }_n(x)$ corresponding to the discrete spectrum. … ►Explicit normalization is given for the second, third, and fourth of these, paragraphs c) and d), below. … ►thus recapitulating, for $Z=1$, line 11 of Table 18.8.1, now shown with explicit normalization for the measure $dr$. … ►Here tridiagonal representations of simple Schrödinger operators play a similar role. … ►The Coulomb–Pollaczek polynomials provide alternate representations of the positive energy Coulomb wave functions of Chapter 33. …