Laguerre
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1: 18.3 Definitions
§18.3 Definitions
►The classical OP’s comprise the Jacobi, Laguerre and Hermite polynomials. … ►Table 18.3.1 provides the traditional definitions of Jacobi, Laguerre, and Hermite polynomials via orthogonality and standardization (§§18.2(i) and 18.2(iii)). … ►For finite power series of the Jacobi, ultraspherical, Laguerre, and Hermite polynomials, see §18.5(iii) (in powers of for Jacobi polynomials, in powers of for the other cases). Explicit power series for Chebyshev, Legendre, Laguerre, and Hermite polynomials for are given in §18.5(iv). …2: 18.4 Graphics
3: 18.36 Miscellaneous Polynomials
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►Similar OP’s can also be constructed for the Laguerre polynomials; see Koornwinder (1984b, (4.8)).
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§18.36(v) Non-Classical Laguerre Polynomials ,
… ►For the Laguerre polynomials this requires, omitting all strictly positive factors, … ►Type I -Laguerre EOP’s
… ►The resulting EOP’s, , satisfy …4: 17.17 Physical Applications
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►See Kassel (1995).
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►It involves -generalizations of exponentials and Laguerre polynomials, and has been applied to the problems of the harmonic oscillator and Coulomb potentials.
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5: 18.41 Tables
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►For () see §14.33.
►Abramowitz and Stegun (1964, Tables 22.4, 22.6, 22.11, and 22.13) tabulates , , , and for .
The ranges of are for and , and for and .
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►For , , and see §3.5(v).
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