6 Exponential, Logarithmic, Sine, and Cosine Integrals Notation 6 Exponential, Logarithmic, Sine, and Cosine Integrals 6.2 Definitions and Interrelations

§6.1 Special Notation

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Keywords:: auxiliary functions, cosine integrals, exponential integrals, logarithmic integral, notation, sine integrals
Permalink:: http://dlmf.nist.gov/6.1
See also:: Annotations for Ch.6

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

$x$	real variable.
$z$	complex variable.
$n$	nonnegative integer.
$\delta$	arbitrary small positive constant.
$\gamma$	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 $\operatorname{Ei}\left(x\right)$ , $E_{1}\left(z\right)$ , and $\operatorname{Ein}\left(z\right)$ ; the logarithmic integral $\operatorname{li}\left(x\right)$ ; the sine integrals $\operatorname{Si}\left(z\right)$ and $\operatorname{si}\left(z\right)$ ; the cosine integrals $\operatorname{Ci}\left(z\right)$ and $\operatorname{Cin}\left(z\right)$ .

6 Exponential, Logarithmic, Sine, and Cosine Integrals 6.2 Definitions and Interrelations

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