§6.19 Tables

§6.19(i) Introduction

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

§6.19(ii) Real Variables

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

• Zhang and Jin (1996, pp. 652, 689) includes $\mathop{\mathrm{Si}\/}\nolimits\!\left(x\right)$, $\mathop{\mathrm{Ci}\/}\nolimits\!\left(x\right)$, $x=0(.5)20(2)30$, 8D; $\mathop{\mathrm{Ei}\/}\nolimits\!\left(x\right)$, $\mathop{E_{1}\/}\nolimits\!\left(x\right)$, $x=[0,100]$, 8S.

§6.19(iii) Complex Variables, $z=x+iy$

• Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of $ze^{z}\mathop{E_{1}\/}\nolimits\!\left(z\right)$, $x=-19(1)20$, $y=0(1)20$, 6D; $e^{z}\mathop{E_{1}\/}\nolimits\!\left(z\right)$, $x=-4(.5)-2$, $y=0(.2)1$, 6D; $\mathop{E_{1}\/}\nolimits\!\left(z\right)+\mathop{\ln\/}\nolimits z$, $x=-2(.5)2.5$, $y=0(.2)1$, 6D.

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