§6.19 Tables

Lebedev and Fedorova (1960) and Fletcher et al. (1962) give comprehensive indexes of mathematical tables. This section lists relevant tables that appeared later.

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  Abramowitz and Stegun (1964, Chapter 5) includes $x^{-1}\mathrm{Si}\left(x\right)$, $-x^{-2}\mathrm{Cin}\left(x\right)$, $x^{-1}\mathrm{Ein}\left(x\right)$, $-x^{-1}\mathrm{Ein}\left(-x\right)$, $x=0(.01)0.5$; $\mathrm{Si}\left(x\right)$, $\mathrm{Ci}\left(x\right)$, $\mathrm{Ei}\left(x\right)$, $E_1\left(x\right)$, $x=0.5(.01)2$; $\mathrm{Si}\left(x\right)$, $\mathrm{Ci}\left(x\right)$, $x{\mathrm{e}}^{-x}\mathrm{Ei}\left(x\right)$, $x{\mathrm{e}}^x{E}_1\left(x\right)$, $x=2(.1)10$; $x\mathrm{f}\left(x\right)$, $x^2\mathrm{g}\left(x\right)$, $x{\mathrm{e}}^{-x}\mathrm{Ei}\left(x\right)$, $x{\mathrm{e}}^x{E}_1\left(x\right)$, $x^{-1}=0(.005)0.1$; $\mathrm{Si}\left(\pi x\right)$, $\mathrm{Cin}\left(\pi x\right)$, $x=0(.1)10$. Accuracy varies but is within the range 8S–11S.

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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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  Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of $z{\mathrm{e}}^z{E}_1\left(z\right)$, $x=-19(1)20$, $y=0(1)20$, 6D; ${\mathrm{e}}^z{E}_1\left(z\right)$, $x=-4(.5)-2$, $y=0(.2)1$, 6D; $E_1\left(z\right)+\ln z$, $x=-2(.5)2.5$, $y=0(.2)1$, 6D.

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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.