Let [$]p(x)[$] be a probability density function (pdf) for a random variable with support on [$]R = (-\infty,\infty)[$]. Then [$]F(x) = \int_{-\infty}^x p(y) \, dy[$] is the (cumulative) distribution function, and [$]\phi(z) = \int_R e^{i z x} p(x) \, dx[$] is the characteristic function.

But, does anybody know a standard name for [$]G(a,b; z) \equiv \int_a^b e^{i z x} p(x) \, dx[$]? Basically, it is the "Fourier transform of the pdf restricted to an interval", which is a mouthful. If not, I am thinking of calling it simply a "restricted characteristic function", but would welcome other naming suggestions if I indeed have to make up a name.