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The Lambert W-function, also called the omega function, is the inverse function of f(W)=We^W. (1) The plot above shows the function along the real axis. The principal value ...

The Mittag-Leffler function (Mittag-Leffler 1903, 1905) is an entire function defined by the series E_alpha(z)=sum_(k=0)^infty(z^k)/(Gamma(alphak+1)) (1) for alpha>0. It is ...

The pathological function f_a(x)=sum_(k=1)^infty(sin(pik^ax))/(pik^a) (originally defined for a=2) that is continuous but differentiable only on a set of points of measure ...

The alternating factorial is defined as the sum of consecutive factorials with alternating signs, a(n)=sum_(k=1)^n(-1)^(n-k)k!. (1) They can be given in closed form as ...

A Bessel function Z_n(x) is a function defined by the recurrence relations Z_(n+1)+Z_(n-1)=(2n)/xZ_n (1) and Z_(n+1)-Z_(n-1)=-2(dZ_n)/(dx). (2) The Bessel functions are more ...

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

The Cantor set T_infty, sometimes also called the Cantor comb or no middle third set (Cullen 1968, pp. 78-81), is given by taking the interval [0,1] (set T_0), removing the ...

Clebsch-Gordan coefficients are mathematical symbol used to integrate products of three spherical harmonics. Clebsch-Gordan coefficients commonly arise in applications ...

The confluent hypergeometric function of the second kind gives the second linearly independent solution to the confluent hypergeometric differential equation. It is also ...

A connex is a geometric form introduced by Clebsch (1872) that included as special cases the curve considered as a point locus and the curve considered as a line envelope ...