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11: 17.15 Generalizations

§17.15 Generalizations

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12: 7.16 Generalized Error Functions

§7.16 Generalized Error Functions

►Generalizations of the error function and Dawson’s integral are ${\int }_0^x{\mathrm{e}}^{-t^p}dt$ and ${\int }_0^x{\mathrm{e}}^{t^p}dt$. …

13: 16.26 Approximations

§16.26 Approximations

►For discussions of the approximation of generalized hypergeometric functions and the Meijer $G$-function in terms of polynomials, rational functions, and Chebyshev polynomials see Luke (1975, §§5.12 - 5.13) and Luke (1977b, Chapters 1 and 9).

14: 3.11 Approximation Techniques

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§3.11(i) Minimax Polynomial Approximations

… ►Then (in general) a better approximation to $p_n(x)$ is given by … ►For general intervals $[a,b]$ we rescale: … ►

§3.11(iii) Minimax Rational Approximations

… ►Then the minimax (or best uniform) rational approximation …

15: Bibliography Q

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“Best possible” upper and lower bounds for the zeros of the Bessel function $J_{\nu }(x)$ . Trans. Amer. Math. Soc. 351 (7), pp. 2833–2859.

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External Links:

ISSN 0002-9947, FullText, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.21(vii).

Encodings:

BibTeX

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16: Need Help?

… ►We have also tried to use the best technologies available in order to make this information useful and accessible. …

17: 24.16 Generalizations

§24.16 Generalizations

… ►For $\mathrm{\ell }=0,1,2,\mathrm{\dots }$, Bernoulli and Euler polynomials of order $\mathrm{\ell }$ are defined respectively by … ► $B_n^{(x)}$ is a polynomial in $x$ of degree $n$. … ►

§24.16(ii) Character Analogs

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§24.16(iii) Other Generalizations

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18: 8.24 Physical Applications

§8.24 Physical Applications

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§8.24(iii) Generalized Exponential Integral

… ►With more general values of $p$, $E_p\left(x\right)$ supplies fundamental auxiliary functions that are used in the computation of molecular electronic integrals in quantum chemistry (Harris (2002), Shavitt (1963)), and also wave acoustics of overlapping sound beams (Ding (2000)).

19: 4.44 Other Applications

§4.44 Other Applications

… ►For applications of generalized exponentials and generalized logarithms to computer arithmetic see §3.1(iv). ►For an application of the Lambert $W$-function to generalized Gaussian noise see Chapeau-Blondeau and Monir (2002). …

20: 16.24 Physical Applications

§16.24 Physical Applications

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§16.24(i) Random Walks

►Generalized hypergeometric functions and Appell functions appear in the evaluation of the so-called Watson integrals which characterize the simplest possible lattice walks. … ►

§16.24(iii) $\mathit{3}j$, $\mathit{6}j$, and $\mathit{9}j$ Symbols

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