Search Results for ""

The nth order Bernstein expansion of a function f(x) in terms of a variable x is given by B_n(f,x)=sum_(j=0)^n(n; j)x^j(1-x)^(n-j)f(j/n), (1) (Gzyl and Palacios 1997, Mathé ...

Given a real number x, find the powers of a base b that will shift the digits of x a number of places n to the left. This is equivalent to solving b^x=b^nx (1) or x=n+log_bx. ...

A member of the smallest algebraically closed subfield L of C which is closed under the exponentiation and logarithm operations.

Expressions of the form lim_(k->infty)x_0+sqrt(x_1+sqrt(x_2+sqrt(...+x_k))) (1) are called nested radicals. Herschfeld (1935) proved that a nested radical of real nonnegative ...

Let a convex polygon be inscribed in a circle and divided into triangles from diagonals from one polygon vertex. The sum of the radii of the circles inscribed in these ...

To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave equation ...

The hyperfactorial (Sloane and Plouffe 1995) is the function defined by H(n) = K(n+1) (1) = product_(k=1)^(n)k^k, (2) where K(n) is the K-function. The hyperfactorial is ...

Mergelyan's theorem can be stated as follows (Krantz 1999). Let K subset= C be compact and suppose C^*\K has only finitely many connected components. If f in C(K) is ...

A number is said to be simply normal to base b if its base-b expansion has each digit appearing with average frequency tending to b^(-1). A normal number is an irrational ...

The Theodorus spiral, also known as the Einstein spiral, Pythagorean spiral, square root spiral, or--to contrast it with certain continuous analogs--the discrete spiral of ...