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31: Bibliography G

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Mutual integrability, quadratic algebras, and dynamical symmetry. Ann. Phys. 217 (1), pp. 1–20.

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External Links:

ISSN 0003-4916, Link, MathReview (A. O. Barut), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX

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32: 2.4 Contour Integrals

… ►with $a$ and $b$ chosen so that the zeros of $\partial p(\alpha ,t)/\partial t$ correspond to the zeros $w_1(\alpha ),w_2(\alpha )$, say, of the quadratic $w^2+2aw+b$. …

33: 18.33 Polynomials Orthogonal on the Unit Circle

… ►After a quadratic transformation (18.2.23) this would express OP’s on $[-1,1]$ with an even orthogonality measure in terms of the ${\varphi }_n$. …

34: 2.3 Integrals of a Real Variable

… ►A uniform approximation can be constructed by quadratic change of integration variable: …

35: 3.11 Approximation Techniques

… ►The iterative process converges locally and quadratically (§3.8(i)). …

36: 19.29 Reduction of General Elliptic Integrals

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37: 36.2 Catastrophes and Canonical Integrals

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38: 18.27 $q$-Hahn Class

… ►The $q$-hypergeometric OP’s comprise the $q$-Hahn class (or $q$-linear lattice class) OP’s and the Askey–Wilson class (or $q$-quadratic lattice class) OP’s (§18.28). …

39: Errata

… ►The specific updates to Chapter 18 include some results for general orthogonal polynomials including quadratic transformations, uniqueness of orthogonality measure and completeness, moments, continued fractions, and some special classes of orthogonal polynomials. …