Search Results for ""

A cyclide is a pair of focal conics which are the envelopes of two one-parameter families of spheres, sometimes also called a cyclid. The cyclide is a quartic surface, and ...

Given relatively prime integers p and q (i.e., (p,q)=1), the Dedekind sum is defined by s(p,q)=sum_(i=1)^q((i/q))(((pi)/q)), (1) where ((x))={x-|_x_|-1/2 x not in Z; 0 x in ...

A plot of the map winding number W resulting from mode locking as a function of Omega for the circle map theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n) (1) with K=1. (Since ...

The number N_d^((b))(n) of digits d in the base-b representation of a number n is called the b-ary digit count for d. The digit count is implemented in the Wolfram Language ...

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

Let the elliptic modulus k satisfy 0<k^2<1, and the Jacobi amplitude be given by phi=amu with -pi/2<phi<pi/2. The incomplete elliptic integral of the first kind is then ...

The Engel expansion, also called the Egyptian product, of a positive real number x is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

The path traced out by a point P on the edge of a circle of radius b rolling on the outside of a circle of radius a. An epicycloid is therefore an epitrochoid with h=b. ...

Let E_1(x) be the En-function with n=1, E_1(x) = int_1^infty(e^(-tx)dt)/t (1) = int_x^infty(e^(-u)du)/u. (2) Then define the exponential integral Ei(x) by E_1(x)=-Ei(-x), (3) ...

The Fox H-function is a very general function defined by where 0<=m<=q, 0<=n<=p, alpha_j,beta_j>0, and a_j,b_j are complex numbers such that no pole of Gamma(b_j-beta_js) for ...