The author of the book I am referring assumes two rational integral functions as shown below
$p_0\cdot x^n+p_1\cdot x^{(n-1)}+p_2\cdot x^{(n-2)}+...+p_n$
$q_0\cdot x^n+q_1\cdot x^{(n-1)}+q_2\cdot x^{(n-2)}+...+q_n$
Is this term old and he means real functions ?; if not, what is meant by rational integral function ?, rational function, integral function ?
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$\begingroup$I think this would be helpful:
Reference: Handbook of Mathematics and Computational Science By John W. Harris, Horst Stöcker.
$\endgroup$ $\begingroup$The heading of chap.4 of Modern Algebra 1 (1949) by Van der Waerden is "Polynomials" in English, and "Ganze rationale Funktionen" in German (). According to Bieberbach (Algebra, 1928) a rational analytic expression is an integral rational function if there are no variable divisors.
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