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Are there some books or articles regarding "polynomials" with non-integer (real) exponents, i.e., $$f(x)=a_1x^{e_1}+a_2x^{e_2}+\dots+a_nx^{e_n},$$ where $e_1,e_2,\dots$ are any real numbers (and $x$ being also real)?

I am mostly interested in theorems regarding the location of the roots, number of the roots, bounds, etc., of such "polynomials". Thanks.

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I think the keyword is exponential polynomial because $x^\alpha=e^{\alpha \log x}$.

Try these papers:

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