Search Results for ""

The Bessel functions of the first kind J_n(x) are defined as the solutions to the Bessel differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+(x^2-n^2)y=0 (1) which are ...

Let a particle travel a distance s(t) as a function of time t (here, s can be thought of as the arc length of the curve traced out by the particle). The speed (the scalar ...

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 ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

By analogy with the sinc function, define the tanc function by tanc(z)={(tanz)/z for z!=0; 1 for z=0. (1) Since tanz/z is not a cardinal function, the "analogy" with the sinc ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

Let V be a vector space over a field K, and let A be a nonempty set. Now define addition p+a in A for any vector a in V and element p in A subject to the conditions: 1. ...

As defined by Kyrmse, a canonical polygon is a closed polygon whose vertices lie on a point lattice and whose edges consist of vertical and horizontal steps of unit length or ...

The cyclic group C_(11) is unique group of group order 11. An example is the integers modulo 11 under addition (Z_(11)). No modulo multiplication group is isomorphic to ...

Taking the ratio x/y of two numbers x and y, also written x÷y. Here, x is called the dividend, y is called the divisor, and x/y is called a quotient. The symbol "/" is called ...