Laguerre
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11: 18.1 Notation
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Classical OP’s
… ►Laguerre: and . ( with is also called Generalized Laguerre.)
-Laguerre: .
12: 18.9 Recurrence Relations and Derivatives
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Laguerre
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18.9.13
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18.9.14
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Laguerre
… ►Further -th derivative formulas relating two different Laguerre polynomials can be obtained from §13.3(ii) by substitution of (13.6.19). …13: 8.7 Series Expansions
§8.7 Series Expansions
►For the functions , , and see (8.4.11), §§10.47(ii), and 18.3, respectively. … ►
8.7.6
, .
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14: 18.5 Explicit Representations
§18.5 Explicit Representations
… ►Laguerre
… ►Similarly in the cases of the ultraspherical polynomials and the Laguerre polynomials we assume that , and , unless stated otherwise. … ►Laguerre
… ►15: 18.21 Hahn Class: Interrelations
16: 18.10 Integral Representations
17: 18.7 Interrelations and Limit Relations
18: 18.11 Relations to Other Functions
19: 18.34 Bessel Polynomials
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►For the confluent hypergeometric function and the generalized hypergeometric function , the Laguerre polynomial and the Whittaker function see §16.2(ii), §16.2(iv), (18.5.12), and (13.14.3), respectively.
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18.34.1
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18.34.7_1
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►expressed in terms of Romanovski–Bessel polynomials, Laguerre polynomials or Whittaker functions, we have
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20: 18.39 Applications in the Physical Sciences
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