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1: 24.20 Tables

… ►Abramowitz and Stegun (1964, Chapter 23) includes exact values of ${\sum }_{k=1}^m{k}^n$, $m=1(1)100$, $n=1(1)10$; ${\sum }_{k=1}^{\mathrm{\infty }}{k}^{-n}$, ${\sum }_{k=1}^{\mathrm{\infty }}{(-1)}^{k-1}{k}^{-n}$, ${\sum }_{k=0}^{\mathrm{\infty }}{(2k+1)}^{-n}$, $n=1,2,\mathrm{\dots }$, 20D; ${\sum }_{k=0}^{\mathrm{\infty }}{(-1)}^k{(2k+1)}^{-n}$, $n=1,2,\mathrm{\dots }$, 18D. …

2: 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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Makinouchi (1966) tabulates all values of $j_{\nu ,m}$ and $y_{\nu ,m}$ in the interval $(0,100)$, with at least 29S. These are for $\nu =0(1)5$, 10, 20; $\nu =\frac{3}{2}$, $\frac{5}{2}$; $\nu =m/n$ with $m=1(1)n-1$ and $n=3(1)8$, except for $\nu =\frac{1}{2}$.

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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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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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3: 28.35 Tables

§28.35 Tables

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Blanch and Clemm (1962) includes values of ${\mathrm{Mc}}_n^{(1)}(x,\sqrt{q})$ and $\mathrm{Mc}_n^{(1)}{}_{}{}^{\prime }(x,\sqrt{q})$ for $n=0(1)15$ with $q=0(.05)1$, $x=0(.02)1$. Also ${\mathrm{Ms}}_n^{(1)}(x,\sqrt{q})$ and $\mathrm{Ms}_n^{(1)}{}_{}{}^{\prime }(x,\sqrt{q})$ for $n=1(1)15$ with $q=0(.05)1$, $x=0(.02)1$. Precision is generally 7D.

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Blanch and Clemm (1965) includes values of ${\mathrm{Mc}}_n^{(2)}(x,\sqrt{q})$, $\mathrm{Mc}_n^{(2)}{}_{}{}^{\prime }(x,\sqrt{q})$ for $n=0(1)7$, $x=0(.02)1$; $n=8(1)15$, $x=0(.01)1$. Also ${\mathrm{Ms}}_n^{(2)}(x,\sqrt{q})$, $\mathrm{Ms}_n^{(2)}{}_{}{}^{\prime }(x,\sqrt{q})$ for $n=1(1)7$, $x=0(.02)1$; $n=8(1)15$, $x=0(.01)1$. In all cases $q=0(.05)1$. Precision is generally 7D. Approximate formulas and graphs are also included.

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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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4: 26.21 Tables

… ►Andrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts $\cancel{\equiv }\pm 2(mod5)$, partitions into parts $\cancel{\equiv }\pm 1(mod5)$, and unrestricted plane partitions up to 100. … ►Goldberg et al. (1976) contains tables of binomial coefficients to $n=100$ and Stirling numbers to $n=40$.

5: 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

… ►In Figures 15.3.5 and 15.3.6, height corresponds to the absolute value of the function and color to the phase. …

6: 5.22 Tables

… ►Abramowitz and Stegun (1964, Chapter 6) tabulates $\mathrm{\Gamma }\left(x\right)$, $\ln \mathrm{\Gamma }\left(x\right)$, $\psi \left(x\right)$, and ${\psi }^{\prime }\left(x\right)$ for $x=1(.005)2$ to 10D; ${\psi }^{\prime \prime }\left(x\right)$ and ${\psi }^{(3)}\left(x\right)$ for $x=1(.01)2$ to 10D; $\mathrm{\Gamma }\left(n\right)$, $1/\mathrm{\Gamma }\left(n\right)$, $\mathrm{\Gamma }\left(n+\frac{1}{2}\right)$, $\psi \left(n\right)$, ${\log }_{10}\mathrm{\Gamma }\left(n\right)$, ${\log }_{10}\mathrm{\Gamma }\left(n+\frac{1}{3}\right)$, ${\log }_{10}\mathrm{\Gamma }\left(n+\frac{1}{2}\right)$, and ${\log }_{10}\mathrm{\Gamma }\left(n+\frac{2}{3}\right)$ for $n=1(1)101$ to 8–11S; $\mathrm{\Gamma }\left(n+1\right)$ for $n=100(100)1000$ to 20S. Zhang and Jin (1996, pp. 67–69 and 72) tabulates $\mathrm{\Gamma }\left(x\right)$, $1/\mathrm{\Gamma }\left(x\right)$, $\mathrm{\Gamma }\left(-x\right)$, $\ln \mathrm{\Gamma }\left(x\right)$, $\psi \left(x\right)$, $\psi \left(-x\right)$, ${\psi }^{\prime }\left(x\right)$, and ${\psi }^{\prime }\left(-x\right)$ for $x=0(.1)5$ to 8D or 8S; $\mathrm{\Gamma }\left(n+1\right)$ for $n=0(1)100(10)250(50)500(100)3000$ to 51S. …

7: 23.17 Elementary Properties

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§23.17(i) Special Values

… ►In (23.17.5) for terms up to $q^{48}$ see Zuckerman (1939), and for terms up to $q^{100}$ see van Wijngaarden (1953). …

8: 6.19 Tables

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Zhang and Jin (1996, pp. 652, 689) includes $\mathrm{Si}\left(x\right)$, $\mathrm{Ci}\left(x\right)$, $x=0(.5)20(2)30$, 8D; $\mathrm{Ei}\left(x\right)$, $E_1\left(x\right)$, $x=[0,100]$, 8S.

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Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of $E_1\left(z\right)$, $\pm x=0.5,1,3,5,10,15,20,50,100$, $y=0(.5)1(1)5(5)30,50,100$, 8S.

9: 8.26 Tables

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Zhang and Jin (1996, Table 3.8) tabulates $\gamma (a,x)$ for $a=0.5,1,3,5,10,25,50,100$, $x=0(.1)1(1)3,5(5)30,50,100$ to 8D or 8S.

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Zhang and Jin (1996, Table 19.1) tabulates $E_n\left(x\right)$ for $n=1,2,3,5,10,15,20$, $x=0(.1)1,1.5,2,3,5,10,20,30,50,100$ to 7D or 8S.

10: 5.17 Barnes’ $G$-Function (Double Gamma Function)

… ►In this equation (and in (5.17.5) below), the $\mathrm{Ln}$’s have their principal values on the positive real axis and are continued via continuity, as in §4.2(i). … ►For Glaisher’s constant see also Greene and Knuth (1982, p. 100) and §2.10(i).