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All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

When |x|<1/2, (1-x)^(-a)_2F_1(a,b;c;-x/(1-x))=_2F_1(a,c-b;c;x).

An adjoint curve which bears a special relation to the base curve.

A plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...

Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.

The ordinary differential equation y^('')+k/xy^'+deltae^y=0.

The study of harmonic functions (also called potential functions).

An algebra in which the associator (x,x,x)=0. The subalgebra generated by one element is associative.

The derivative of the power x^n is given by d/(dx)(x^n)=nx^(n-1).

A ring for which the product of any pair of ideals is zero only if one of the two ideals is zero. All simple rings are prime.