Rodrigues formula

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1: 18.20 Hahn Class: Explicit Representations

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§18.20(i) Rodrigues Formulas

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Table 18.20.1: Krawtchouk, Meixner, and Charlier OP’s: Rodrigues formulas (18.20.1).

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$p_n(x)$	$F(x)$	${\kappa }_n$
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2: 18.5 Explicit Representations

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§18.5(ii) Rodrigues Formulas

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Table 18.5.1: Classical OP’s: Rodrigues formulas (18.5.5).

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$p_n(x)$	$w(x)$	$F(x)$	${\kappa }_n$
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3: 18.3 Definitions

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As given by a Rodrigues formula (18.5.5).

… ►For representations of the polynomials in Table 18.3.1 by Rodrigues formulas, see §18.5(ii). …

4: 14.7 Integer Degree and Order

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§14.7(ii) Rodrigues-Type Formulas

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5: 18.10 Integral Representations

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6: 18.39 Applications in the Physical Sciences

… ►see Bethe and Salpeter (1957, p. 13), Pauling and Wilson (1985, pp. 130, 131); and noting that this differs from the Rodrigues formula of (18.5.5) for the Laguerre OP’s, in the omission of an $n!$ in the denominator. …

7: 18.18 Sums

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§18.18(iv) Connection and Inversion Formulas

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§18.18(v) Linearization Formulas

… ►Formula (18.18.27) is known as the Hille–Hardy formula. … ►Formula (18.18.28) is known as the Mehler formula. …

8: Bibliography W

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Quadrature formulas for oscillatory integral transforms. Numer. Math. 39 (3), pp. 351–360.

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External Links:

ISSN 0029-599X, Document, MathReview (A.J. Rodrigues), ZentralBlatt

Referenced by:

§10.74(vii), §3.5(vii).

Encodings:

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