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An asymmetrical apodization function defined by M(x,b,d)={0 for x<-b; (x-b)/(2b) for -b<x<b; 1 for b<x<b+2d; 0 for x<b+2d, (1) where the two-sided portion is 2b long (total) ...

An Artin L-function over the rationals Q encodes in a generating function information about how an irreducible monic polynomial over Z factors when reduced modulo each prime. ...

A function is termed regular iff it is analytic and single-valued throughout a region R.

Let g:R->R be a function and let h>0, and define the cardinal series of g with respect to the interval h as the formal series sum_(k=-infty)^inftyg(kh)sinc((x-kh)/h), where ...

The distribution function D(x), also called the cumulative distribution function (CDF) or cumulative frequency function, describes the probability that a variate X takes on a ...

A number theoretic function is a function whose domain is the set of positive integers.

A function f(x) is said to be strictly decreasing on an interval I if f(b)<f(a) for all b>a, where a,b in I. On the other hand, if f(b)<=f(a) for all b>a, the function is ...

A function f(x) is said to be strictly increasing on an interval I if f(b)>f(a) for all b>a, where a,b in I. On the other hand, if f(b)>=f(a) for all b>a, the function is ...

A function whose value decreases more quickly than any polynomial is said to be an exponentially decreasing function. The prototypical example is the function e^(-x), plotted ...

A function whose value increases more quickly than any polynomial is said to be an exponentially increasing function. The prototypical example is the function e^x, plotted ...