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The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as ...

Schmidt (1993) proposed the problem of determining if for any integer r>=2, the sequence of numbers {c_k^((r))}_(k=1)^infty defined by the binomial sums sum_(k=0)^n(n; ...

Let A be an n×n real square matrix with n>=2 such that |sum_(i=1)^nsum_(j=1)^na_(ij)s_it_j|<=1 (1) for all real numbers s_1, s_2, ..., s_n and t_1, t_2, ..., t_n such that ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

An algorithm which finds a polynomial recurrence for terminating hypergeometric identities of the form sum_(k)(n; ...

alpha_n(z) = int_1^inftyt^ne^(-zt)dt (1) = n!z^(-(n+1))e^(-z)sum_(k=0)^(n)(z^k)/(k!). (2) It is equivalent to alpha_n(z)=E_(-n)(z), (3) where E_n(z) is the En-function.

A map F from R^n to R^n is area-preserving if m(F^(-1)(A))=m(A) for every subregion A of R^n, where m(A) is the n-dimensional measure of A. A linear transformation is ...

For a simple continued fraction x=[a_0,a_1,...] with convergents p_n/q_n, the fundamental recurrence relation is given by p_nq_(n-1)-p_(n-1)q_n=(-1)^(n+1).

A delta sequence is a sequence of strongly peaked functions for which lim_(n->infty)int_(-infty)^inftydelta_n(x)f(x)dx=f(0) (1) so that in the limit as n->infty, the ...

The equations are x = ((lambda-lambda_0)(1+costheta))/(sqrt(2+pi)) (1) y = (2theta)/(sqrt(2+pi)), (2) where theta is the solution to theta+sintheta=(1+1/2pi)sinphi. (3) This ...