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11: 10.75 Tables

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Zhang and Jin (1996, pp. 185–195) tabulates $J_n\left(x\right)$, $J_n^{\prime }\left(x\right)$, $Y_n\left(x\right)$, $Y_n^{\prime }\left(x\right)$, $n=0(1)10(10)50,100$, $x=1$, 5, 10, 25, 50, 100, 9S; $J_{n+\alpha }\left(x\right)$, $J_{n+\alpha }^{\prime }\left(x\right)$, $Y_{n+\alpha }\left(x\right)$, $Y_{n+\alpha }^{\prime }\left(x\right)$, $n=0(1)5,10,30,50,100$, $\alpha =\frac{1}{4},\frac{1}{3},\frac{1}{2},\frac{2}{3},\frac{3}{4}$, $x=1,5,10,50$, 8S; real and imaginary parts of $J_{n+\alpha }\left(z\right)$, $J_{n+\alpha }^{\prime }\left(z\right)$, $Y_{n+\alpha }\left(z\right)$, $Y_{n+\alpha }^{\prime }\left(z\right)$, $n=0(1)15,20(10)50,100$, $\alpha =0,\frac{1}{2}$, $z=4+2\mathrm{i}$, $20+10\mathrm{i}$, 8S.

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Morgenthaler and Reismann (1963) tabulates $j_{n,m}^{\prime }$ for $n=21(1)51$ and , 7-10S.

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Döring (1971) tabulates the first 100 values of $\nu$ $(>1)$ for which $J_{-\nu }^{\prime }\left(x\right)$ has the double zero $x=\nu$, 10D.

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Zhang and Jin (1996, pp. 240–250) tabulates $I_n\left(x\right)$, $I_n^{\prime }\left(x\right)$, $K_n\left(x\right)$, $K_n^{\prime }\left(x\right)$, $n=0(1)10(10)50,100$, $x=1,5,10,25,50,100$, 9S; $I_{n+\alpha }\left(x\right)$, $I_{n+\alpha }^{\prime }\left(x\right)$, $K_{n+\alpha }\left(x\right)$, $K_{n+\alpha }^{\prime }\left(x\right)$, $n=0(1)5$, 10, 30, 50, 100, $\alpha =\frac{1}{4}$, $\frac{1}{3}$, $\frac{1}{2}$, $\frac{2}{3}$, $\frac{3}{4}$, $x=1$, 5, 10, 50, 8S; real and imaginary parts of $I_{n+\alpha }\left(z\right)$, $I_{n+\alpha }^{\prime }\left(z\right)$, $K_{n+\alpha }\left(z\right)$, $K_{n+\alpha }^{\prime }\left(z\right)$, $n=0(1)15$, 20(10)50, 100, $\alpha =0,\frac{1}{2}$, $z=4+2\mathrm{i},20+10\mathrm{i}$, 8S.

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The main tables in Abramowitz and Stegun (1964, Chapter 10) give ${𝗃}_n\left(x\right)$, ${𝗒}_n\left(x\right)$ $n=0(1)8$, $x=0(.1)10$, 5–8S; ${𝗃}_n\left(x\right)$, ${𝗒}_n\left(x\right)$ $n=0(1)20(10)50$, 100, $x=1,2,5,10,50,100$, 10S; ${𝗂}_n^{(1)}\left(x\right)$, ${𝗄}_n\left(x\right)$, $n=0,1,2$, $x=0(.1)5$, 4–9D; ${𝗂}_n^{(1)}\left(x\right)$, ${𝗄}_n\left(x\right)$, $n=0(1)20(10)50$, 100, $x=1,2,5,10,50,100$, 10S. (For the notation see §10.1 and §10.47(ii).)

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12: 7.23 Tables

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Zhang and Jin (1996, pp. 637, 639) includes $(2/\sqrt{\pi }){\mathrm{e}}^{-x^2}$, $\mathrm{erf}x$, $x=0(.02)1(.04)3$, 8D; $C\left(x\right)$, $S\left(x\right)$, $x=0(.2)10(2)100(100)500$, 8D.

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Fettis et al. (1973) gives the first 100 zeros of $\mathrm{erf}z$ and $w\left(z\right)$ (the table on page 406 of this reference is for $w\left(z\right)$, not for $\mathrm{erfc}z$), 11S.

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13: 11.14 Tables

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Agrest et al. (1982) tabulates ${𝐇}_n\left(x\right)$ and ${\mathrm{e}}^{-x}{𝐋}_n\left(x\right)$ for $n=0,1$ and $x=0(.001)5(.005)15(.01)100$ to 11D.

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Barrett (1964) tabulates ${𝐋}_n\left(x\right)$ for $n=0,1$ and $x=0.2(.005)4(.05)10(.1)19.2$ to 5 or 6S, $x=6(.25)59.5(.5)100$ to 2S.

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Agrest et al. (1982) tabulates ${\int }_0^x{𝐇}_0\left(t\right)dt$ and ${\mathrm{e}}^{-x}{\int }_0^x{𝐋}_0\left(t\right)dt$ for $x=0(.001)5(.005)15(.01)100$ to 11D.

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14: Foreword

… ►That 1046-page tome proved to be an invaluable reference for the many scientists and engineers who use the special functions of applied mathematics in their day-to-day work, so much so that it became the most widely distributed and most highly cited NIST publication in the first 100 years of the institution’s existence. …

15: Charles W. Clark

… ►Clark received the R&D 100 Award, Distinguished Presidential Rank Award of the U. …

16: 28.35 Tables

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National Bureau of Standards (1967) includes the eigenvalues $a_n\left(q\right)$, $b_n\left(q\right)$ for $n=0(1)3$ with $q=0(.2)20(.5)37(1)100$, and $n=4(1)15$ with $q=0(2)100$; Fourier coefficients for ${\mathrm{ce}}_n(x,q)$ and ${\mathrm{se}}_n(x,q)$ for $n=0(1)15$, $n=1(1)15$, respectively, and various values of $q$ in the interval $[0,100]$; joining factors $g_{e,n}(\sqrt{q})$, $f_{e,n}(\sqrt{q})$ for $n=0(1)15$ with $q=0(.5\text{ to }10)100$ (but in a different notation). Also, eigenvalues for large values of $q$. Precision is generally 8D.

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Blanch and Clemm (1969) includes eigenvalues $a_n\left(q\right)$, $b_n\left(q\right)$ for $q=\rho {\mathrm{e}}^{\mathrm{i}\varphi }$, $\rho =0(.5)25$, $\varphi =5^{\circ }(5^{\circ }){90}^{\circ }$, $n=0(1)15$; 4D. Also $a_n\left(q\right)$ and $b_n\left(q\right)$ for $q=\mathrm{i}\rho$, $\rho =0(.5)100$, $n=0(2)14$ and $n=2(2)16$, respectively; 8D. Double points for $n=0(1)15$; 8D. Graphs are included.

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17: 27.21 Tables

… ►Lehmer (1914) lists all primes up to 100 06721. …

18: Publications

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From B-Spline Mesh Generation to Effective Visualizations for the NIST Digital Library of Mathematical Functions, in Curve and Surface Design, Proceedings of the Sixth International Conference on Curves and Surfaces, Avignon, France June 29–July 5, 2006, pp. 235–243.

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19: 15.3 Graphics

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Figure 15.3.1: $F(\frac{4}{3},\frac{9}{16};\frac{14}{5};x),-100\le x\le 1$. Magnify

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20: Frank W. J. Olver

… ►A highly regarded expositor, Olver was author of more than 100 technical articles. …