Search Results for ""

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

If, after constructing a difference table, no clear pattern emerges, turn the paper through an angle of 60 degrees and compute a new table. If necessary, repeat the process. ...

Let a set of random variates X_1, X_2, ..., X_n have a probability function P(X_1=x_1,...,X_n=x_n)=(N!)/(product_(i=1)^(n)x_i!)product_(i=1)^ntheta_i^(x_i) (1) where x_i are ...

|_n]!={n! for n>=0; ((-1)^(-n-1))/((-n-1)!) for n<0. (1) The Roman factorial arises in the definition of the harmonic logarithm and Roman coefficient. It obeys the identities ...

(1) for p in [-1/2,1/2], where delta is the central difference and S_(2n+1) = 1/2(p+n; 2n+1) (2) S_(2n+2) = p/(2n+2)(p+n; 2n+1), (3) with (n; k) a binomial coefficient.

If algebraic integers alpha_1, ..., alpha_n are linearly independent over Q, then e^(alpha_1), ..., e^(alpha_n) are algebraically independent over Q. The ...

A lattice embedding is a one-to-one lattice homomorphism.

The least common denominator of a collection of fractions (p_1)/(q_1),...,(p_n)/(q_n) is the least common multiple LCM(q_1,...,q_n) of their denominators.

Let (X,A,mu) and (Y,B,nu) be measure spaces. A measurable rectangle is a set of the form A×B for A in A and B in B.

For K a given knot in S^3, choose a Seifert surface M^2 in S^3 for K and a bicollar M^^×[-1,1] in S^3-K. If x in H_1(M^^) is represented by a 1-cycle in M^^, let x^+ denote ...