Answer to Question #100319 in Physics for Kishwer

Question

What is algebraic transcendental function?

Answer 1

Transcendental function is a function not expressible as a finite combination of the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extracting a root. Examples include the functions $\log x, \sin x, \cos x, e^x$ and any functions containing them. 

Algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power.