Search Results for "Euler Maclaurin Integration Formulas"

The rth sample raw moment m_r^' of a sample with sample size n is defined as m_r^'=1/nsum_(k=1)^nx_k^r. (1) The sample raw moments are unbiased estimators of the population ...

11 21 8 61 22 58 241 52 328 444 1201 114 1452 4400 3708 7201 240 5610 32120 58140 33984 5040 (1) The second-order Eulerian triangle (OEIS A008517) is the number triangle ...

Let I_A, I_B, and I_C be the vertices of the inner Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines ...

The second Napoleon point N^', also called the inner Napoleon point, is the concurrence of lines drawn between polygon vertices of a given triangle DeltaABC and the opposite ...

The second Steiner circle (a term coined here for the first time) is the circumcircle of the Steiner triangle DeltaS_AS_BS_C. Its center has center function ...

Let p(n) be the first prime which follows a prime gap of n between consecutive primes. Shanks' conjecture holds that p(n)∼exp(sqrt(n)). Wolf conjectures a slightly different ...

For any M, there exists a t^' such that the sequence n^2+t^', where n=1, 2, ... contains at least M primes.

A transformation that preserves angles and changes all distances in the same ratio, called the ratio of magnification. A similarity can also be defined as a transformation ...

Given a set P with |P|=p elements consisting of c_1 numbers 1, c_2 numbers 2, ..., and c_n numbers n and c_1+c_2+...+c_n=p, find the number of permutations with k-1 rises ...

Given a triangle DeltaABC with inner and outer Soddy centers S and S^', respectively, the inner Soddy triangle DeltaPQR (respectively, outer Soddy triangle DeltaP^'Q^'R^') is ...