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A matrix whose elements may contain complex numbers. The matrix product of two 2×2 complex matrices is given by (1) where R_(11) = ...

Faà di Bruno's formula gives an explicit equation for the nth derivative of the composition f(g(t)). If f(t) and g(t) are functions for which all necessary derivatives are ...

A Gaussian integer is a complex number a+bi where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often ...

An algorithm for finding closed form hypergeometric identities. The algorithm treats sums whose successive terms have ratios which are rational functions. Not only does it ...

The Church-Turing thesis (formerly commonly known simply as Church's thesis) says that any real-world computation can be translated into an equivalent computation involving a ...

The improvement of the convergence properties of a series, also called convergence acceleration or accelerated convergence, such that a series reaches its limit to within ...

Wirsing (1974) showed, among other results, that if F_n(x) is the Gauss-Kuzmin distribution, then lim_(n->infty)(F_n(x)-lg(1+x))/((-lambda)^n)=Psi(x), (1) where ...

A statement which appears self-contradictory or contrary to expectations, also known as an antinomy. Curry (1977, p. 5) uses the term pseudoparadox to describe an apparent ...

A string figure is any pattern produced when a looped string is spanned between two hands and is twisted and woven in various manners around the fingers and the wrists. The ...

The Barnes G-function is an analytic continuation of the G-function defined in the construction of the Glaisher-Kinkelin constant G(n)=([Gamma(n)]^(n-1))/(H(n-1)) (1) for ...