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Given a Taylor series f(z)=sum_(n=0)^inftyC_nz^n=sum_(n=0)^inftyC_nr^ne^(intheta), (1) where the complex number z has been written in the polar form z=re^(itheta), examine ...

An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements. For example, there are two distinct ...

A triangle in which all three angles are acute angles. A triangle which is neither acute nor a right triangle (i.e., it has an obtuse angle) is called an obtuse triangle. ...

The word adjoint has a number of related meanings. In linear algebra, it refers to the conjugate transpose and is most commonly denoted A^(H). The analogous concept applied ...

Let X be an alphabet (i.e., a finite and nonempty set), and call its member letters. A word on X is a finite sequence of letters a_1...a_n, where a_1,...,a_n in X. Denote the ...

A function representable as a generalized Fourier series. Let R be a metric space with metric rho(x,y). Following Bohr (1947), a continuous function x(t) for (-infty<t<infty) ...

An alternating knot is a knot which possesses a knot diagram in which crossings alternate between under- and overpasses. Not all knot diagrams of alternating knots need be ...

R. C. Read defined the anarboricity of a graph G as the maximum number of edge-disjoint nonacyclic (i.e., cyclic) subgraphs of G whose union is G (Harary and Palmer 1973, p. ...

The Andrews-Gordon identity (Andrews 1974) is the analytic counterpart of Gordon's combinatorial generalization of the Rogers-Ramanujan identities (Gordon 1961). It has a ...

Construct a chain C of 2n components in a solid torus V. Now thicken each component of C slightly to form a chain C_1 of 2n solid tori in V, where pi_1(V-C_1)=pi_1(V-C) via ...