Definition:Polynomial Function/Real/Definition 1

Definition

Let $S \subset \R$ be a subset of the real numbers.

A real polynomial function on $S$ is a function $f: S \to \R$ for which there exist:

a natural number $n\in \N$

real numbers $a_0, \ldots, a_n \in \R$

such that for all $x \in S$:

$\map f x = \ds \sum_{k \mathop = 0}^n a_k x^k$

where $\sum$ denotes indexed summation.

Also known as

A polynomial function is often simply called polynomial.

Some sources refer to it as a rational integral function.

Also see

• Equivalence of Definitions of Real Polynomial Function

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 3$: Natural Numbers: Exercise $\S 3.11 \ (3)$
• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 7.6$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): function (map, mapping)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): function (map, mapping)