Search Results for ""

The problem of finding the mean triangle area of a triangle with vertices picked inside a triangle with unit area was proposed by Watson (1865) and solved by Sylvester. It ...

Let L(x) denote the Rogers L-function defined in terms of the usual dilogarithm by L(x) = 6/(pi^2)[Li_2(x)+1/2lnxln(1-x)] (1) = ...

The axiom of Zermelo-Fraenkel set theory which asserts the existence for any set a and a formula A(y) of a set x consisting of all elements of a satisfying A(y), exists x ...

A transformation formula for continued fractions (Lorentzen and Waadeland 1992) which can, for example, be used to prove identities such as ...

Roman (1984, p. 26) defines "the" binomial identity as the equation p_n(x+y)=sum_(k=0)^n(n; k)p_k(y)p_(n-k)(x). (1) Iff the sequence p_n(x) satisfies this identity for all y ...

For a general quadrilateral with sides of length a, b, c, and d, the area K is given by (1) where s=1/2(a+b+c+d) (2) is the semiperimeter, A is the angle between a and d, and ...

The characteristic polynomial is the polynomial left-hand side of the characteristic equation det(A-lambdaI)=0, (1) where A is a square matrix and I is the identity matrix of ...

Using a Chebyshev polynomial of the first kind T(x), define c_j = 2/Nsum_(k=1)^(N)f(x_k)T_j(x_k) (1) = 2/Nsum_(k=1)^(N)f[cos{(pi(k-1/2))/N}]cos{(pij(k-1/2))/N}. (2) Then f(x) ...

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...

Let n points xi_1, ..., xi_n be randomly distributed on a domain S, and let H be some event that depends on the positions of the n points. Let S^' be a domain slightly ...