Abstract
This chapter provides an overview of algebraic relationships and addition theorems. It discusses the transcendental functions. Two transcendental entire functions canbe related by an algebraic equation. It further discusses algebraic relationships between the values of a single entire function at different values of its argument. There is no nonconstant entire function that has two periods, the ratio of which is not a rational number. All the formulas in trigonometry are the results of the addition theorems. The Weierstrass theorem is discussed which states that if an entire function f(z) obeys an algebraic addition theorem, it is either an algebraic polynomial, which as a special case may be a constant, or a trigonometric polynomial.
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