# §13.16 Integral Representations

## §13.16(i) Integrals Along the Real Line

In this subsection see §§10.2(ii), 10.25(ii) for the functions , , and , and §§15.1, 15.2(i) for .

13.16.4.

where is arbitrary, .

## §13.16(ii) Contour Integrals

For contour integral representations combine (13.14.2) and (13.14.3) with §13.4(ii). See Buchholz (1969, §2.3), Erdélyi et al. (1953a, §6.11.3), and Slater (1960, Chapter 3). See also §13.16(iii).

## §13.16(iii) Mellin–Barnes Integrals

If , then

where the contour of integration separates the poles of from those of .

If , then

where the contour of integration separates the poles of from those of .

where the contour of integration passes all the poles of on the right-hand side.