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Ramanujan developed a number of interesting closed-form expressions for generalized continued fractions. These include the almost integers ...

The unitary divisor function sigma_k^*(n) is the analog of the divisor function sigma_k(n) for unitary divisors and denotes the sum-of-kth-powers-of-the-unitary divisors ...

A semiperfect magic cube, sometimes also called an "Andrews cube" (Gardner 1976; Gardner 1988, p. 219) is a magic cube for which the cross section diagonals do not sum to the ...

A vector derivative is a derivative taken with respect to a vector field. Vector derivatives are extremely important in physics, where they arise throughout fluid mechanics, ...

The central beta function is defined by beta(p)=B(p,p), (1) where B(p,q) is the beta function. It satisfies the identities beta(p) = 2^(1-2p)B(p,1/2) (2) = ...

A coequalizer of a pair of maps f,g:X->Y in a category is a map c:Y->C such that 1. c degreesf=c degreesg, where degrees denotes composition. 2. For any other map c^':Y->C^' ...

A tool with two arms joined at their ends which can be used to draw circles. In geometric constructions, the classical Greek rules stipulate that the compass cannot be used ...

_0F_1(;a;z)=lim_(q->infty)_1F_1(q;a;z/q). (1) It has a series expansion _0F_1(;a;z)=sum_(n=0)^infty(z^n)/((a)_nn!) (2) and satisfies z(d^2y)/(dz^2)+a(dy)/(dz)-y=0. (3) It is ...

Given a triangle, draw a Cevian to one of the bases that divides it into two triangles having congruent incircles. The positions and sizes of these two circumcircles can then ...

An unsolvable problem in logic dating back to the ancient Greeks and quoted, for example, by German philosopher Carl von Prantl (1855). The dilemma consists of a crocodile ...