Weierstrass elliptic functions p(z) := p(z, [c.sub.2], [c.sub.3]) have an addition formula as below:
Applying the addition formula, we can rewrite it as
Weierstrass elliptic functions [??](z) := [??](z, [g.sub.2], [g.sub.3]) have two successive degeneracies and addition formula
The final step of adding the federal and state taxes in Cell B14 is using another addition formula
After each list is compiled, a new generation or an adjoining culture finds a better way of constructing the tables, sometimes rediscovering old ways, yet all mimicking the reasoning and style of Ptolemy's Almagest and its recursive construction by way of versions of the half angle formulas and the addition formulas
, whose modern day representatives are
These addition formulas are proved in an operational way, so no certain convergence region can be given; in general small function arguments work best.
As long as no addition formulas for these q-trigonometric functions exist, they are not very interesting from an operational point of view.
* New properties, e.g., integral representations and addition formulas
, have been discovered.