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sum_(k=0)^(infty)[((m)_k)/(k!)]^3 = 1+(m/1)^3+[(m(m+1))/(1·2)]^3+... (1) = (Gamma(1-3/2m))/([Gamma(1-1/2m)]^3)cos(1/2mpi), (2) where (m)_k is a Pochhammer symbol and Gamma(z) ...

Let g(x_1,...,x_n,y) be a function such that for any x_1, ..., x_n, there is at least one y such that g(x_1,...,x_n,y)=0. Then the mu-operator muy(g(x_1,...,x_n,y)=0) gives ...

Müntz's theorem is a generalization of the Weierstrass approximation theorem, which states that any continuous function on a closed and bounded interval can be uniformly ...

A multidimensional point process is a measurable function from a probability space (Omega,A,P) into (X,Sigma) where X is the set of all finite or countable subsets of R^d not ...

The multinomial coefficients (n_1,n_2,...,n_k)!=((n_1+n_2+...+n_k)!)/(n_1!n_2!...n_k!) (1) are the terms in the multinomial series expansion. In other words, the number of ...

Consider a reference triangle DeltaABC with circumcenter O and orthocenter H, and let DeltaA^*B^*C^* be its reflection triangle. Then Musselman's theorem states that the ...

Let Omega be a space with measure mu>=0, and let Phi(P,Q) be a real function on the product space Omega×Omega. When (mu,nu) = intintPhi(P,Q)dmu(Q)dnu(P) (1) = ...

Polynomials s_k(x;a) which form the Sheffer sequence for g(t) = ((e^t-1)/t)^(-a) (1) f(t) = e^t-1 (2) which have generating function ...

A direct search method of optimization that works moderately well for stochastic problems. It is based on evaluating a function at the vertices of a simplex, then iteratively ...

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...