tables of zeros

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21: 29.3 Definitions and Basic Properties

… ►In this table the nonnegative integer $m$ corresponds to the number of zeros of each Lamé function in $(0,K)$, whereas the superscripts $2m$, $2m+1$, or $2m+2$ correspond to the number of zeros in $[0,2K)$. …

22: 10.76 Approximations

… ►Luke (1971b, a, 1972), Luke (1975, Tables 9.1, 9.2, 9.5, 9.6, 9.11–9.15, 9.17–9.21), Weniger and Čížek (1990), Németh (1992, Chapters 4–6). ►

Real Variable and Order $:$ Zeros

… ►Luke (1975, Tables 9.3, 9.4, 9.7–9.9, 9.16, 9.22), Németh (1992, Chapter 10). … ►Luke (1975, Tables 9.23–9.28), Coleman and Monaghan (1983), Coleman (1987), Zhang (1996), Zhang and Belward (1997). … ►Luke (1975, Table 9.10), Németh (1992, Chapter 9).

23: Guide to Searching the DLMF

… ►From there you can also access an advanced search page where you can control certain settings, narrowing the search to certain chapters, or restricting the results to equations, graphs, tables, or bibliographic items. ►

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24: 3.8 Nonlinear Equations

… ►As in the case of Table 3.8.1 the quadratic nature of convergence is clearly evident: as the zero is approached, the number of correct decimal places doubles at each iteration. …

25: 18.41 Tables

§18.41 Tables

… ►For $P_n\left(x\right)$ ($={𝖯}_n\left(x\right)$) see §14.33. … ►

§18.41(ii) Zeros

… ►See also Abramowitz and Stegun (1964, Tables 25.4, 25.9, and 25.10). ►

§18.41(iii) Other Tables

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26: 10.21 Zeros

§10.21 Zeros

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§10.21(vi) McMahon’s Asymptotic Expansions for Large Zeros

… ► … ►The zeros of the functions …

27: 19.14 Reduction of General Elliptic Integrals

… ►The choice among 21 transformations for final reduction to Legendre’s normal form depends on inequalities involving the limits of integration and the zeros of the cubic or quartic polynomial. A similar remark applies to the transformations given in Erdélyi et al. (1953b, §13.5) and to the choice among explicit reductions in the extensive table of Byrd and Friedman (1971), in which one limit of integration is assumed to be a branch point of the integrand at which the integral converges. …

28: 18.3 Definitions

… ►In addition to the orthogonal property given by Table 18.3.1, the Chebyshev polynomials $T_n\left(x\right)$, $n=0,1,\mathrm{\dots },N$, are orthogonal on the discrete point set comprising the zeros $x_{N+1,n},n=1,2,\mathrm{\dots },N+1$, of $T_{N+1}\left(x\right)$: …

29: Bibliography C

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A table of elliptic integrals of the second kind. Math. Comp. 49 (180), pp. 595–606, S13–S17.

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External Links:

ISSN 0025-5718, Document, Supplement, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§19.29(i).

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A table of elliptic integrals of the third kind. Math. Comp. 51 (183), pp. 267–280, S1–S5.

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ISSN 0025-5718, Document, Supplement, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§19.29(i).

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The analyticity of cross-product Bessel function zeros. Proc. Cambridge Philos. Soc. 62, pp. 215–226.

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MathReview (R. G. Langebartel), ZentralBlatt

Referenced by:

§10.21(x).

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On zeros of the hypergeometric function. Serdica 7 (3), pp. 243–249.

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ISSN 0204-4140, MathReview (R. G. Buschman), ZentralBlatt

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§15.13.

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Tables of Jacobian Elliptic Functions Whose Arguments are Rational Fractions of the Quarter Period. National Physical Laboratory Mathematical Tables, Vol. 7, Her Majesty’s Stationery Office, London.

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ISBN 00-791-1158-0, MathReview (John Todd), ZentralBlatt

Referenced by:

§22.20(vii), §22.21.

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30: 12.19 Tables

§12.19 Tables

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Zhang and Jin (1996, pp. 455–473) includes $U(\pm n-\frac{1}{2},x)$, $V(\pm n-\frac{1}{2},x)$, $U(\pm \nu -\frac{1}{2},x)$, $V(\pm \nu -\frac{1}{2},x)$, and derivatives, $\nu =n+\frac{1}{2}$, $n=0(1)10(10)30$, $x=0.5,1,5,10,30,50$, 8S; $W(a,\pm x)$, $W(-a,\pm x)$, and derivatives, $a=h(1)5+h$, $x=0.5,1$ and $a=h(1)5+h$, $x=5$, $h=0,0.5$, 8S. Also, first zeros of $U(a,x)$, $V(a,x)$, and of derivatives, $a=-6(.5)-1$, 6D; first three zeros of $W(a,-x)$ and of derivative, $a=0(.5)4$, 6D; first three zeros of $W(-a,\pm x)$ and of derivative, $a=0.5(.5)5.5$, 6D; real and imaginary parts of $U(a,z)$, $a=-1.5(1)1.5$, $z=x+\mathrm{i}y$, $x=0.5,1,5,10$, $y=0(.5)10$, 8S.

►For other tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).