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Generalized polynomials (polynomials with exponents which ar...

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Generalized polynomials (polynomials with exponents which ar...

I am dealing with a function thats looks exactly like a polynomial, but has exponents that are Real numbers instead of the usual Natural numbers. What is this type of function called? Are there any theorems related to the number of roots for such a function? Thanks.

PS1: It is not sufficient to re-label the exponents as a Rational number to convert the function to a polynomial, since this leaves Irrational exponents unaccounted for.

PS2: In the case of a Monomial of this function, it is a Power function.


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