§6.1 Special Notation

Keywords:: cosine integrals, exponential integrals, logarithmic integral, sine integrals
Permalink:: http://dlmf.nist.gov/6.1

(For other notation see Notation for the Special Functions.)

$x$	real variable.
$z$	complex variable.
$n$	nonnegative integer.
$\delta$	arbitrary small positive constant.
$\EulerConstant$	Euler’s constant (§5.2(ii)).

Unless otherwise noted, primes indicate derivatives with respect to the argument.

The main functions treated in this chapter are the exponential integrals $\mathop{\mathrm{Ei}\/}\nolimits\!\left(x\right)$ , $\mathop{E_{1}\/}\nolimits\!\left(z\right)$ , and $\mathop{\mathrm{Ein}\/}\nolimits\!\left(z\right)$ ; the logarithmic integral $\mathop{\mathrm{li}\/}\nolimits\!\left(x\right)$ ; the sine integrals $\mathop{\mathrm{Si}\/}\nolimits\!\left(z\right)$ and $\mathop{\mathrm{si}\/}\nolimits\!\left(z\right)$ ; the cosine integrals $\mathop{\mathrm{Ci}\/}\nolimits\!\left(z\right)$ and $\mathop{\mathrm{Cin}\/}\nolimits\!\left(z\right)$ .