Editing Power series (section)

=== On the set of exponents ===

Negative powers are not permitted in an ordinary power series; for instance, <math display="inline">x^{-1} + 1 + x^{1} + x^{2} + \cdots</math> is not considered a power series (although it is a [[Laurent series]]). Similarly, fractional powers such as <math display="inline">x^\frac{1}{2}</math> are not permitted; fractional powers arise in [[Puiseux series]]. The coefficients <math display="inline"> a_n</math> must not depend on {{nowrap|<math display="inline">x</math>,}} thus for instance <math display="inline">\sin(x) x + \sin(2x) x^2 + \sin(3x) x^3 + \cdots </math> is not a power series.