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The fractional derivative of f(t) of order mu>0 (if it exists) can be defined in terms of the fractional integral D^(-nu)f(t) as D^muf(t)=D^m[D^(-(m-mu))f(t)], (1) where m is ...

An integral equation of the form phi(x)=f(x)+lambdaint_(-infty)^inftyK(x,t)phi(t)dt (1) phi(x)=1/(sqrt(2pi))int_(-infty)^infty(F(t)e^(-ixt)dt)/(1-sqrt(2pi)lambdaK(t)). (2) ...

A free Abelian group is a group G with a subset which generates the group G with the only relation being ab=ba. That is, it has no group torsion. All such groups are a direct ...

An equation of the form f(x,y,...)=0, where f contains a finite number of independent variables, known functions, and unknown functions which are to be solved for. Many ...

As defined by Erdélyi et al. (1981, p. 20), the G-function is given by G(z)=psi_0(1/2+1/2z)-psi_0(1/2z), (1) where psi_0(z) is the digamma function. Integral representations ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...

Gabriel's horn, also called Torricelli's trumpet, is the surface of revolution of the function y=1/x about the x-axis for x>=1. It is therefore given by parametric equations ...

Finch (2010) gives an overview of known results for random Gaussian triangles. Let the vertices of a triangle in n dimensions be normal (normal) variates. The probability ...

At rational arguments p/q, the digamma function psi_0(p/q) is given by psi_0(p/q)=-gamma-ln(2q)-1/2picot(p/qpi) +2sum_(k=1)^([q/2]-1)cos((2pipk)/q)ln[sin((pik)/q)] (1) for ...

A solid such that the area A_y of any section parallel to and a distance y from a fixed plane can be expressed as A_y=ay^3+by^2+cy+d. The volume of such a solid is the same ...