Quite often, algebraic functions are algebraic expressions using a finite number of terms and involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Some algebraic functions, however, cannot be expressed by such finite expressions.
Source: wiktionary
The value of an algebraic function at an algebraic number is always an algebraic number.
Source: wiktionary
1989, Manuel Bronstein, An Algorithm for the Integration of Elementary Functions, James H. Davenport (editor), EUROCAL '87: European Conference on Computer Algebra, Proceedings, Springer, LNCS 378, page 491,
Trager (1984) recently gave a new algorithm for the indefinite integration of algebraic functions.
Source: wiktionary
1992, A. A. Goldberg, V. A. Pyana, Uniqueness Theorems for Algebraic Functions, A. B. Sossinsky (translation editor), Boris Yakovlevich Levin (editor), Entire and Subharmonic Functions, American Mathematical Society, page 199,
It is known that the algebraic function w=w(z) enables one to determine the polynomial P(z,w) up to a constant factor.
Source: wiktionary
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