little q-Jacobi polynomials
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11: 34.8 Approximations for Large Parameters
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34.8.1
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►and the symbol denotes a quantity that tends to zero as the parameters tend to infinity, as in §2.1(i).
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12: 2.10 Sums and Sequences
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►As in §24.2, let and denote the th Bernoulli number and polynomial, respectively, and the th Bernoulli periodic function .
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(a)
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►From §24.12(i), (24.2.2), and (24.4.27), is of constant sign .
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On the strip , is analytic in its interior, is continuous on its closure, and as , uniformly with respect to .
Example
►Let be a constant in and denote the Legendre polynomial of degree . …13: 33.10 Limiting Forms for Large or Large
14: 18.28 Askey–Wilson Class
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Duality
… ►§18.28(v) Continuous -Ultraspherical Polynomials
… ►These polynomials are also called Rogers polynomials. ►§18.28(vi) Continuous -Hermite Polynomials
… ►From Askey–Wilson to Little -Jacobi
…15: 2.1 Definitions and Elementary Properties
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2.1.2
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►The symbols and can be used generically.
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►This result also holds with both ’s replaced by ’s.
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16: 28.29 Definitions and Basic Properties
17: 18.2 General Orthogonal Polynomials
§18.2 General Orthogonal Polynomials
… ►Kernel Polynomials
… ►It is to be noted that, although formally correct, the results of (18.2.30) are of little utility for numerical work, as Hankel determinants are notoriously ill-conditioned. … ► … ►Sheffer Polynomials
…18: 18.40 Methods of Computation
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§18.40(i) Computation of Polynomials
►Orthogonal polynomials can be computed from their explicit polynomial form by Horner’s scheme (§1.11(i)). … … ►There are many ways to implement these first two steps, noting that the expressions for and of equation (18.2.30) are of little practical numerical value, see Gautschi (2004) and Golub and Meurant (2010). … ►The example chosen is inversion from the for the weight function for the repulsive Coulomb–Pollaczek, RCP, polynomials of (18.39.50). …19: 15.12 Asymptotic Approximations
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►For the more general case in which and see Wagner (1990).
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►See also Dunster (1999) where the asymptotics of Jacobi polynomials is described; compare (15.9.1).
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