# §25.5 Integral Representations

## §25.5(i) In Terms of Elementary Functions

Throughout this subsection .

## §25.5(ii) In Terms of Other Functions

where

For see §20.2(i). For similar representations involving other theta functions see Erdélyi et al. (1954a, p. 339).

## §25.5(iii) Contour Integrals

25.5.20,

where the integration contour is a loop around the negative real axis; it starts at , encircles the origin once in the positive direction without enclosing any of the points , , …, and returns to . Equivalently,

The contour here is any loop that encircles the origin in the positive direction not enclosing any of the points , , ….