Hermite polynomial case
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1: 12.1 Special Notation
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►Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values.
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►Whittaker’s notation is useful when is a nonnegative integer (Hermite polynomial case).
2: 12.7 Relations to Other Functions
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§12.7(i) Hermite Polynomials
…3: 12.11 Zeros
4: 18.3 Definitions
§18.3 Definitions
►Table 18.3.1 provides the definitions of Jacobi, Laguerre, and Hermite polynomials via orthogonality and normalization (§§18.2(i) and 18.2(iii)). This table also includes the following special cases of Jacobi polynomials: ultraspherical, Chebyshev, and Legendre. … ►For exact values of the coefficients of the Jacobi polynomials , the ultraspherical polynomials , the Chebyshev polynomials and , the Legendre polynomials , the Laguerre polynomials , and the Hermite polynomials , see Abramowitz and Stegun (1964, pp. 793–801). … ►Legendre polynomials are special cases of Legendre functions, Ferrers functions, and associated Legendre functions (§14.7(i)). …5: 13.18 Relations to Other Functions
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►Special cases are the error functions
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§13.18(v) Orthogonal Polynomials
►Special cases of §13.18(iv) are as follows. … ►Hermite Polynomials
… ►Laguerre Polynomials
…6: 13.6 Relations to Other Functions
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►Special cases are the error functions
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►and in the case that is an integer we have
…Note that (13.6.11_1) and (13.6.11_2) are special cases of (13.11.1) and (13.11.2), respectively
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►Special cases of §13.6(iv) are as follows.
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Hermite Polynomials
…7: 18.6 Symmetry, Special Values, and Limits to Monomials
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►For Jacobi, ultraspherical, Chebyshev, Legendre, and Hermite polynomials, see Table 18.6.1.
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Laguerre
… ► ►§18.6(ii) Limits to Monomials
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18.6.4
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8: 18.15 Asymptotic Approximations
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