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Concept# Addition theorem

Summary

In mathematics, an addition theorem is a formula such as that for the exponential function:
:ex + y = ex · ey,
that expresses, for a particular function f, f(x + y) in terms of f(x) and f(y). Slightly more generally, as is the case with the trigonometric functions sin and cos, several functions may be involved; this is more apparent than real, in that case, since there cos is an algebraic function of sin (in other words, we usually take their functions both as defined on the unit circle).
The scope of the idea of an addition theorem was fully explored in the nineteenth century, prompted by the discovery of the addition theorem for elliptic functions. To "classify" addition theorems it is necessary to put some restriction on the type of function G admitted, such that
:F(x + y) = G(F(x), F(y)).
In this identity one can assume that F and G are vector-valued (have several components). An algebraic addition theorem is one in whic

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