There are a number of notational systems for the Jacobi theta functions.
The notations given in the Wikipedia article define the original function which is equivalent to where
However, a similar notation is defined somewhat differently in Whittaker and Watson, p. 487: This notation is attributed to "Hermite, H.J.S.
Whittaker and Watson, Abramowitz and Stegun, and Gradshteyn and Ryzhik all follow Tannery and Molk, in which Note that there is no factor of π in the argument as in the previous definitions.
Whittaker and Watson refer to still other definitions of
The warning in Abramowitz and Stegun, "There is a bewildering variety of notations...in consulting books caution should be exercised," may be viewed as an understatement.
It is incumbent upon the author to state what definition of