Search Results for ""

Let alpha(x) be a step function with the jump j(x)=(N; x)p^xq^(N-x) (1) at x=0, 1, ..., N, where p>0,q>0, and p+q=1. Then the Krawtchouk polynomial is defined by ...

Let E(k) and K(k) be complete elliptic integrals of the first and second kinds, with E^'(k) and K^'(k) the complementary integrals. Then ...

The quadrifolium is the 4-petalled rose curve having n=2. It has polar equation r=asin(2theta) (1) and Cartesian equation (x^2+y^2)^3=4a^2x^2y^2. (2) The area of the ...

Given a hypergeometric or generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;z), the corresponding regularized hypergeometric function is defined by where ...

Rule 250 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

The most common form of cosine integral is Ci(x) = -int_x^infty(costdt)/t (1) = gamma+lnx+int_0^x(cost-1)/tdt (2) = 1/2[Ei(ix)+Ei(-ix)] (3) = -1/2[E_1(ix)+E_1(-ix)], (4) ...

The computation of points or values between ones that are known or tabulated using the surrounding points or values. In particular, given a univariate function f=f(x), ...

A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely ...

For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...

An elliptic integral is an integral of the form int(A(x)+B(x)sqrt(S(x)))/(C(x)+D(x)sqrt(S(x)))dx, (1) or int(A(x)dx)/(B(x)sqrt(S(x))), (2) where A(x), B(x), C(x), and D(x) ...