polynomial of $x$?

Question

I want to refer to functions of the form $f(x) = \sum_{i=1}^n a_i x^{\alpha_i}$ where $\alpha_i < 1$.

This is not a polynomial, because $\alpha_i$ could be just real arbitrary numbers (though positive ones). Is there a name for this class of functions that I can refer to? Wikipedia does claim these are not polynomials.

I want to change the name of this thread since polynomials by definition have only nonnegative integer powers of the variable, but I can't think of a better title... :( — J. M. ain't a mathematician, Oct 24 '10 at 23:46
I stated it as a question... so perhaps it is okay. "is it a polynomial of $x$?" — normvector, Oct 25 '10 at 12:46

score 3 · Answer 1 · answered Oct 24 '10 at 23:07

3

In 1983 they still had no official name, see for example this paper by Peter Borwein.

answered Oct 24 '10 at 23:07

Yuval Filmus

57,157

Thanks. From the title of the paper, don't you think it is called "polynomial with variable exponents?" – normvector Oct 24 '10 at 23:17
(though, it seems like this name was rarely used, according to google.) – normvector Oct 24 '10 at 23:18

score 1 · Answer 2 · answered Feb 02 '12 at 19:41

1

Such a function is called "sum of power functions". I don't know of any shorter name. If $\alpha_i<1$ is not a typo, then it's a sum of power functions with exponents less than $1$.

answered Feb 02 '12 at 19:41

polynomial of $x$?

2 Answers2