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At the age of 17, Bernard Mares proposed the definite integral (Borwein and Bailey 2003, p. 26; Bailey et al. 2006) C_2 = int_0^inftycos(2x)product_(n=1)^(infty)cos(x/n)dx ...

The inner Soddy center (or inner Soddy point) is the center of the inner Soddy circle. It is equivalent to the equal detour point X_(175) (Kimberling 1994) and has equivalent ...

Integration under the integral sign is the use of the identity int_a^bdxint_(alpha_0)^alphaf(x,alpha)dalpha=int_(alpha_0)^alphadalphaint_a^bf(x,alpha)dx (1) to compute an ...

Divide a set of data into two groups (high and low) of equal size at the statistical median if there is an even number of data points, or two groups consisting of points on ...

If p_1, ..., p_n are positive numbers which sum to 1 and f is a real continuous function that is convex, then f(sum_(i=1)^np_ix_i)<=sum_(i=1)^np_if(x_i). (1) If f is concave, ...

The simplest interpretation of the Kronecker delta is as the discrete version of the delta function defined by delta_(ij)={0 for i!=j; 1 for i=j. (1) The Kronecker delta is ...

Legendre's formula counts the number of positive integers less than or equal to a number x which are not divisible by any of the first a primes, (1) where |_x_| is the floor ...

A closed interval corresponding to a finite portion of an infinite line. Line segments are generally labeled with two letters corresponding to their endpoints, say A and B, ...

The Ljubljana graph is a graph on 112 vertices that is the third smallest cubic semisymmetric graph. It was discovered by Brouwer et al. (1993) and rediscovered by Conder et ...

By analogy with the log sine function, define the log cosine function by C_n=int_0^(pi/2)[ln(cosx)]^ndx. (1) The first few cases are given by C_1 = -1/2piln2 (2) C_2 = ...