A period is a number that can be expressed as an integral of an algebraic function over an algebraic domain.
A period is defined as "a complex number whose real and imaginary parts are values of absolutely convergent integrals of rational functions with rational coefficients, over domains in $\mathbb R^n$ given by polynomial inequalities with rational coefficients."
More compactly: A period is a number that can be expressed as an integral of an algebraic function over an algebraic domain.
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