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Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements. Antichains are also called Sperner systems in older literature ...

A sequence s_n^((lambda))(x)=[h(t)]^lambdas_n(x), where s_n(x) is a Sheffer sequence, h(t) is invertible, and lambda ranges over the real numbers is called a Steffensen ...

An Appell sequence is a Sheffer sequence for (g(t),t). Roman (1984, pp. 86-106) summarizes properties of Appell sequences and gives a number of specific examples. The ...

If A is a normed algebra, a net {e_i} in A is called an approximate identity for A if sup_(i)|e_i|<infty and if for each a in A, e_ia->a and ae_i->a. Though this definition ...

The associated Legendre differential equation is a generalization of the Legendre differential equation given by d/(dx)[(1-x^2)(dy)/(dx)]+[l(l+1)-(m^2)/(1-x^2)]y=0, (1) which ...

Informally, the term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). A line or curve A that is asymptotic to given ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

Let phi:M->M be a C^1 diffeomorphism on a compact Riemannian manifold M. Then phi satisfies Axiom A if the nonwandering set Omega(phi) of phi is hyperbolic and the periodic ...

Propositional calculus, first-order logic, and other theories in mathematical logic are defined by their axioms (or axiom schemata, plural: axiom schemata) and inference ...

A method of solving combinatorial problems by means of an algorithm which is allowed to run forward until a dead end is reached, at which point previous steps are retraced ...