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The regularized gamma functions are defined by P(a,z) = (gamma(a,z))/(Gamma(a)) (1) Q(a,z) = (Gamma(a,z))/(Gamma(a)), (2) where gamma(a,z) and Gamma(a,z) are incomplete gamma ...

Given a hypergeometric or generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;z), the corresponding regularized hypergeometric function is defined by where ...

The Rogers mod 14 identities are a set of three Rogers-Ramanujan-like identities given by A(q) = sum_(n=0)^(infty)(q^(n^2))/((q;q)_n(q;q^2)_n) (1) = ...

A sequence of approximations a/b to sqrt(n) can be derived by factoring a^2-nb^2=+/-1 (1) (where -1 is possible only if -1 is a quadratic residue of n). Then ...

The vector Laplacian can be generalized to yield the tensor Laplacian A_(munu;lambda)^(;lambda) = (g^(lambdakappa)A_(munu;lambda))_(;kappa) (1) = ...

The term "total curvature" is used in two different ways in differential geometry. The total curvature, also called the third curvature, of a space curve with line elements ...

(d^2u)/(dz^2)+(du)/(dz)+(k/z+(1/4-m^2)/(z^2))u=0. (1) Let u=e^(-z/2)W_(k,m)(z), where W_(k,m)(z) denotes a Whittaker function. Then (1) becomes ...

In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3, .... In formal set theory, a cardinal number (also called "the ...

The point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...