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When A and B are self-adjoint operators, e^(t(A+B))=lim_(n->infty)(e^(tA/n)e^(tB/n))^n.

A specific type of ultraproduct that can be used to construct nonstandard universes and obtain the transfer principle as a corollary of Łoś' theorem for ultraproducts.

A function of a single variable (e.g., f(x), g(z), theta(xi), etc.).

A function f(x) is said to be antiperiodic with antiperiod p if -f(x)=f(x+np) for n=1, 3, .... For example, the sine function sinx is antiperiodic with period pi (as well as ...

The study of the nature and properties of bifurcations.

f(x)=C_psiint_(-infty)^inftyint_(-infty)^infty<f,psi^(a,b)>psi^(a,b)(x)a^(-2)dadb, where psi^(a,b)(x)=|a|^(-1/2)psi((x-b)/a). This result was originally derived using ...

A set within which the values of a function lie (as opposed to the range, which is the set of values that the function actually takes).

Given a series of the form A(z)=sum_(k)a_kz^k, the notation [z^k](A(z)) is used to indicate the coefficient a_k (Sedgewick and Flajolet 1996). This corresponds to the Wolfram ...

Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...

For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...