tops

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7 matching pages

1: 22.19 Physical Applications

… ►

§22.19(iv) Tops

…

2: 16.2 Definition and Analytic Properties

… ►Suppose first one or more of the top parameters

a_{j}

is a nonpositive integer. … ►However, when one or more of the top parameters

a_{j}

is a nonpositive integer the series terminates and the generalized hypergeometric function is a polynomial in

z

. …

3: 37.19 Other Orthogonal Polynomials of $d$ Variables

… ►Just as the classical OPs fit into the Askey scheme (see §18.19 and Figure 18.21.1) with Wilson and Racah polynomials on top, the Jacobi polynomials on the simplex fit into a scheme of OPs defined as products of one-variable OPs belonging to the Askey scheme by formulas somewhat resembling (37.14.7). …

4: 18.40 Methods of Computation

… ►The bottom and top of the steps at the

x_{i}

are lower and upper bounds to

\int_{a}^{x_{i}}\,\mathrm{d}\mu(x)

as made explicit via the Chebyshev inequalities discussed by Shohat and Tamarkin (1970, pp. 42–43). …

5: Bibliography

… ►

M. Audin (1999) Spinning Tops: A Course on Integrable Systems. Cambridge Studies in Advanced Mathematics, Vol. 51, Cambridge University Press, Cambridge.

ⓘ

External Links:: ISBN 0-521-56129-9; 0-521-77919-7, MathReview (Emma Previato), ZentralBlatt
Referenced by:: §22.19(iv).
Encodings:: BibTeX

…

6: 16.4 Argument Unity

… ►The last condition is equivalent to the sum of the top parameters plus

2

equals the sum of the bottom parameters, that is, the series is 2-balanced. …

7: 18.27 $q$ -Hahn Class

… ►The generic (top level) cases are the

q

-Hahn polynomials and the big

q

-Jacobi polynomials, each of which depends on three further parameters. …