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The important binomial theorem states that sum_(k=0)^n(n; k)r^k=(1+r)^n. (1) Consider sums of powers of binomial coefficients a_n^((r)) = sum_(k=0)^(n)(n; k)^r (2) = ...

The reflexive closure of a binary relation R on a set X is the minimal reflexive relation R^' on X that contains R. Thus aR^'a for every element a of X and aR^'b for distinct ...

The reflexive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same reflexive closure as R. Thus aR^'b for any elements a and b of X, ...

The inverse of the Laplace transform, given by F(t)=1/(2pii)int_(gamma-iinfty)^(gamma+iinfty)e^(st)f(s)ds, where gamma is a vertical contour in the complex plane chosen so ...

Let B, A, and e be square matrices with e small, and define B=A(I+e), (1) where I is the identity matrix. Then the inverse of B is approximately B^(-1)=(I-e)A^(-1). (2) This ...

A relation R on a set S is irreflexive provided that no element is related to itself; in other words, xRx for no x in S.

A relation R on a set S is reflexive provided that xRx for every x in S.

A reflexive relation.

A relation R on a set S is transitive provided that for all x, y and z in S such that xRy and yRz, we also have xRz.

An algorithm for finding integer relations whose running time is bounded by a polynomial in the number of real variables (Ferguson and Bailey 1992). Unfortunately, it is ...