html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 EllipticTheta

Identities involving the group of functions

Basic Algebraic Identities

Relations involving squares

Relations involving quartic powers

For theta1(z,q)

For theta2(z,q)

For theta3(z,q)

For theta4(z,q)

For mixed pairs

Relation between the four theta functions with zero argument

Double angle formulas

For theta1(z,q)

For theta2(z,q)

For theta3(z,q)

For theta4(z,q)

The 16 fundamental algebraic identities (from Enneper)

Four linear combinations of the fundamental identities

Alternative version of fundamental identities (from Tannery and Molk)

Automatically generated triple addition formulas (using 16 fundamental relations)

Automatically generated addition formulas with two variables

Automatically generated double angle formulas

Identities involving transformation of nome q

Equations for z->2z, q->q4

Equations for z->2z, q->q2

General argument

Argument equal to zero

Equations for q->q1/2

General argument

Argument equal to zero

Equations involving integer powers of q