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The analytic summation of a hypergeometric series. Powerful general techniques of hypergeometric summation include Gosper's algorithm, Sister Celine's method, Wilf-Zeilberger ...

A pair of values x and y one or both of which is complex.

A linear transformation of period two. Since a linear transformation has the form, lambda^'=(alphalambda+beta)/(gammalambda+delta), (1) applying the transformation a second ...

Let R be a plane region bounded above by a continuous curve y=f(x), below by the x-axis, and on the left and right by x=a and x=b, then the volume of the solid of revolution ...

Let f and g be nonnegative and continuous functions on the closed interval [a,b], then the solid of revolution obtained by rotating the curves f(x) and g(x) about the x-axis ...

The set lambda of linear Möbius transformations w which satisfy w(t)=(at+b)/(ct+d), where a and d are odd and b and c are even. lambda is a subgroup of the modular group ...

A technically defined group characterizing a system of linear differential equations y_j^'=sum_(k=1)^na_(jk)(x)y_k for j=1, ..., n, where a_(jk) are complex analytic ...

Generalizes the secant method of root finding by using quadratic 3-point interpolation q=(x_n-x_(n-1))/(x_(n-1)-x_(n-2)). (1) Then define A = ...

An analytic refinement of results from complex analysis such as those codified by Picard's little theorem, Picard's great theorem, and the Weierstrass-Casorati theorem.

A metric space Z^^ in which the closure of a congruence class B(j,m) is the corresponding congruence class {x in Z^^|x=j (mod m)}.