Legendre polynomials
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1: 18.3 Definitions
§18.3 Definitions
… ►Name | Constraints | ||||||
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Legendre | |||||||
Shifted Legendre | |||||||
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2: 18.30 Associated OP’s
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Associated Legendre Polynomials
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18.30.6
.
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18.30.7
►(These polynomials are not to be confused with associated Legendre functions §14.3(ii).)
►For further results on associated Legendre polynomials see Chihara (1978, Chapter VI, §12); on associated Jacobi polynomials, see Wimp (1987) and Ismail and Masson (1991).
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3: 18.41 Tables
4: 10.59 Integrals
5: 10.60 Sums
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►Then with again denoting the Legendre polynomial of degree ,
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10.60.1
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10.60.2
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10.60.7
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10.60.8
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6: 14.7 Integer Degree and Order
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§14.7(i)
… ►where is the Legendre polynomial of degree . For additional properties of see Chapter 18. … ►
14.7.4
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14.7.11
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7: 10.54 Integral Representations
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10.54.2
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10.54.3
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►For the Legendre polynomial
and the associated Legendre function see §§18.3 and 14.21(i), with and .
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