6 Exponential, Logarithmic, Sine, and Cosine Integrals Computation 6.18 Methods of Computation 6.20 Approximations

§6.19 Tables

Permalink:: http://dlmf.nist.gov/6.19

§6.19(i) Introduction
§6.19(ii) Real Variables
§6.19(iii) Complex Variables,

§6.19(i) Introduction

Permalink:: http://dlmf.nist.gov/6.19.i

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

Keywords:: auxiliary functions for sine and cosine integrals, cosine integrals, exponential integrals, sine integrals
Permalink:: http://dlmf.nist.gov/6.19.ii

Abramowitz and Stegun (1964, Chapter 5) includes $x^{{-1}}\mathop{\mathrm{Si}\/}\nolimits\!\left(x\right)$ , $-x^{{-2}}\mathop{\mathrm{Cin}\/}\nolimits\!\left(x\right)$ , $x^{{-1}}\mathop{\mathrm{Ein}\/}\nolimits\!\left(x\right)$ , $-x^{{-1}}\mathop{\mathrm{Ein}\/}\nolimits\!\left(-x\right)$ , ; $\mathop{\mathrm{Si}\/}\nolimits\!\left(x\right)$ , $\mathop{\mathrm{Ci}\/}\nolimits\!\left(x\right)$ , $\mathop{\mathrm{Ei}\/}\nolimits\!\left(x\right)$ , $\mathop{E_{1}\/}\nolimits\!\left(x\right)$ , ; $\mathop{\mathrm{Si}\/}\nolimits\!\left(x\right)$ , $\mathop{\mathrm{Ci}\/}\nolimits\!\left(x\right)$ , $xe^{{-x}}\mathop{\mathrm{Ei}\/}\nolimits\!\left(x\right)$ , $xe^{x}\mathop{E_{1}\/}\nolimits\!\left(x\right)$ , ; $x\mathop{\mathrm{f}\/}\nolimits\!\left(x\right)$ , $x^{2}\mathop{\mathrm{g}\/}\nolimits\!\left(x\right)$ , $xe^{{-x}}\mathop{\mathrm{Ei}\/}\nolimits\!\left(x\right)$ , $xe^{x}\mathop{E_{1}\/}\nolimits\!\left(x\right)$ , $x^{{-1}}=0(.005)0.1$ ; $\mathop{\mathrm{Si}\/}\nolimits\!\left(\pi x\right)$ , $\mathop{\mathrm{Cin}\/}\nolimits\!\left(\pi x\right)$ , . Accuracy varies but is within the range 8S–11S.
Zhang and Jin (1996, pp. 652, 689) includes $\mathop{\mathrm{Si}\/}\nolimits\!\left(x\right)$ , $\mathop{\mathrm{Ci}\/}\nolimits\!\left(x\right)$ , , 8D; $\mathop{\mathrm{Ei}\/}\nolimits\!\left(x\right)$ , $\mathop{E_{1}\/}\nolimits\!\left(x\right)$ , , 8S.

§6.19(iii) Complex Variables,

Keywords:: exponential integrals
Permalink:: http://dlmf.nist.gov/6.19.iii

Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of $ze^{z}\mathop{E_{1}\/}\nolimits\!\left(z\right)$ , , , 6D; $e^{z}\mathop{E_{1}\/}\nolimits\!\left(z\right)$ , , , 6D; $\mathop{E_{1}\/}\nolimits\!\left(z\right)+\mathop{\ln\/}\nolimits z$ , , , 6D.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of $\mathop{E_{1}\/}\nolimits\!\left(z\right)$ , $\pm x=0.5,1,3,5,10,15,20,50,100$ , , 8S.