The notions of small φ sign-polynomial expansion g(x + y) = g(x) + g(y) + Σn≥1 pn(small φ sign(x))yn/n! + r(x,y), and multiplicative addition theorems G(x + y) = G(x)G(y) Πk=1N Ψk(small φ signk(x)small φ signk(y)), are introduced and characterization of some small φ sign-polynomial expansions and multiplicative addition theorems are obtained.
- Addition theorems
- Baker-Akhiezer functions
- Landen transform
- Multiplicative addition theorems
- Small φ sign-polynomial expansion
- Weierstrass and Jacobi elliptic functions