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The term "Euler function" may be used to refer to any of several functions in number theory and the theory of special functions, including 1. the totient function phi(n), ...

The kei_nu(z) function is defined as the imaginary part of e^(-nupii/2)K_nu(ze^(pii/4))=ker_nu(z)+ikei_nu(z), (1) where K_nu(z) is a modified Bessel function of the second ...

A power mean is a mean of the form M_p(a_1,a_2,...,a_n)=(1/nsum_(k=1)^na_k^p)^(1/p), (1) where the parameter p is an affinely extended real number and all a_k>=0. A power ...

A q-analog of Gauss's theorem due to Jacobi and Heine, _2phi_1(a,b;c;q,c/(ab))=((c/a;q)_infty(c/b;q)_infty)/((c;q)_infty(c/(ab);q)_infty) (1) for |c/(ab)|<1 (Gordon and ...

The Chu-Vandermonde identity _2F_1(-n,b;c;1)=((c-b)_n)/((c)_n) (1) (for n in Z^+) is a special case of Gauss's hypergeometric theorem _2F_1(a,b;c;1) = ((c-b)_(-a))/((c)_(-a)) ...

A plane curve is a curve that lies in a single plane. A plane curve may be closed or open. Curves which are interesting for some reason and whose properties have therefore ...

The closed cyclic self-intersecting hexagon formed by joining the adjacent antiparallels in the construction of the cosine circle. The sides of this hexagon have the property ...

A special case of the Artin L-function for the polynomial x^2+1. It is given by L(s)=product_(p odd prime)1/(1-chi^-(p)p^(-s)), (1) where chi^-(p) = {1 for p=1 (mod 4); -1 ...

A G-space is a special type of T1-Space. Consider a point x and a homeomorphism of an open neighborhood V of x onto an open set of R^n. Then a space is a G-space if, for any ...

The four-dimensional version of the gradient, encountered frequently in general relativity and special relativity, is del _mu=[1/cpartial/(partialt); partial/(partialx); ...