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The integral transform defined by g(x)=int_1^inftyt^(1/4-nu/2)(t-1)^(1/4-nu/2)P_(-1/2+ix)^(nu-1/2)(2t-1)f(t)dt (Samko et al. 1993, p. 761) or ...

A variable x is memoryless with respect to t if, for all s with t!=0, P(x>s+t|x>t)=P(x>s). (1) Equivalently, (P(x>s+t,x>t))/(P(x>t)) = P(x>s) (2) P(x>s+t) = P(x>s)P(x>t). (3) ...

Let G be a graph with A and B two disjoint n-tuples of graph vertices. Then either G contains n pairwise disjoint AB-paths, each connecting a point of A and a point of B, or ...

The tensor product between modules A and B is a more general notion than the vector space tensor product. In this case, we replace "scalars" by a ring R. The familiar ...

A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) ...

Let f(z) be an analytic function of z, regular in the half-strip S defined by a<x<b and y>0. If f(z) is bounded in S and tends to a limit l as y->infty for a certain fixed ...

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 multiplicative number theoretic function is a number theoretic function f that has the property f(mn)=f(m)f(n) (1) for all pairs of relatively prime positive integers m and ...

The Narayan number N(n,k) for n=1, 2, ... and k=1, ..., n gives a solution to several counting problems in combinatorics. For example, N(n,k) gives the number of expressions ...

A type of mathematical result which is considered by most logicians as more natural than the metamathematical incompleteness results first discovered by Gödel. Finite ...