Editing Theta function (section)

==Relation to the Weierstrass elliptic function==
The theta function was used by Jacobi to construct (in a form adapted to easy calculation) [[Jacobi's elliptic functions|his elliptic functions]] as the quotients of the above four theta functions, and could have been used by him to construct [[Weierstrass's elliptic functions]] also, since

:<math>\wp(z;\tau) = -\big(\log \vartheta_{11}(z;\tau)\big)'' + c</math>

where the second derivative is with respect to {{mvar|z}} and the constant {{mvar|c}} is defined so that the [[Laurent expansion]] of {{math|℘(''z'')}} at {{math|''z'' {{=}} 0}} has zero constant term.