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In the fields of functional and harmonic analysis, the Littlewood-Paley decomposition is a particular way of decomposing the phase plane which takes a single function and ...

The dilogarithm Li_2(z) is a special case of the polylogarithm Li_n(z) for n=2. Note that the notation Li_2(x) is unfortunately similar to that for the logarithmic integral ...

delta(r)=sqrt(r)-2alpha(r), where alpha(r) is the elliptic alpha function.

An elliptic function with no poles in a fundamental cell is a constant.

The general function y(a,b,c,d)=csin{pi/(b-a)[((b-a)x/d+a)^2-a^2]}.

where R[nu]>-1, |argp|<pi/4, and a, b>0, J_nu(z) is a Bessel function of the first kind, and I_nu(z) is a modified Bessel function of the first kind.

A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and ...

A function f(x) is said to be nondecreasing on an interval I if f(b)>=f(a) for all b>a, where a,b in I. Conversely, a function f(x) is said to be nonincreasing on an interval ...

A function f(x) is said to be nonincreasing on an interval I if f(b)<=f(a) for all b>a, where a,b in I. Conversely, a function f(x) is said to be nondecreasing on an interval ...

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...