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Suppose W is the set of all complex-valued functions f on the interval [0,2pi] of the form f(t)=sum_(k=-infty)^inftyalpha_ke^(ikt) (1) for t in [0,2pi], where the alpha_k in ...

Let f(x) be a real continuous monotonic strictly increasing function on the interval [0,a] with f(0)=0 and b<=f(a), then ab<=int_0^af(x)dx+int_0^bf^(-1)(y)dy, where f^(-1)(y) ...

A zero tensor is a tensor of any rank and with any pattern of covariant and contravariant indices all of whose components are equal to 0 (Weinberg 1972, p. 38).

Written in the notation of partial derivatives, the d'Alembertian square ^2 in a flat spacetime is defined by square ^2=del ^2-1/(c^2)(partial^2)/(partialt^2), where c is the ...

The symbol used by engineers and some physicists to denote i, the imaginary number sqrt(-1). j is probably preferred over i because the symbol i (or I) is commonly used to ...

Let y_n be a complex number for 1<=n<=N and let y_n=0 if n<1 or n>N. Then (Montgomery 2001).

Let L(x) denote the Rogers L-function defined in terms of the usual dilogarithm by L(x) = 6/(pi^2)[Li_2(x)+1/2lnxln(1-x)] (1) = ...

A branch point whose neighborhood of values wrap around the range a finite number of times p as their complex arguments theta varies from 0 to a multiple of 2pi is called an ...

An automorphic function f(z) of a complex variable z is one which is analytic (except for poles) in a domain D and which is invariant under a countably infinite group of ...

A Banach algebra is an algebra B over a field F endowed with a norm ||·|| such that B is a Banach space under the norm ||·|| and ||xy||<=||x||||y||. F is frequently taken to ...