L%E2%80%99H%C3%B4pital%20rule%20for%20derivatives
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1: 18.4 Graphics
2: 18.36 Miscellaneous Polynomials
§18.36(v) Non-Classical Laguerre Polynomials ,
… ►For the Laguerre polynomials this requires, omitting all strictly positive factors, … ►implying that, for , the orthogonality of the with respect to the Laguerre weight function , . …These results are proven in Everitt et al. (2004), via construction of a self-adjoint Sturm–Liouville operator which generates the polynomials, self-adjointness implying both orthogonality and completeness. … ►The resulting EOP’s, , satisfy …3: 23.14 Integrals
4: 18.41 Tables
5: 11.14 Tables
Abramowitz and Stegun (1964, Chapter 12) tabulates , , and for and , to 6D or 7D.
Agrest et al. (1982) tabulates and for and to 11D.
Zhang and Jin (1996) tabulates and for and to 8D or 7S.
Abramowitz and Stegun (1964, Chapter 12) tabulates and for to 5D or 7D; , , and for to 6D.
Agrest et al. (1982) tabulates and for to 11D.
6: 11.15 Approximations
Luke (1975, pp. 416–421) gives Chebyshev-series expansions for , , , and , , for ; , , , and , , ; the coefficients are to 20D.
MacLeod (1993) gives Chebyshev-series expansions for , , , and , , ; the coefficients are to 20D.
Newman (1984) gives polynomial approximations for for , , and rational-fraction approximations for for , . The maximum errors do not exceed 1.2×10⁻⁸ for the former and 2.5×10⁻⁸ for the latter.