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By analogy with the sinc function, define the tanc function by tanc(z)={(tanz)/z for z!=0; 1 for z=0. (1) Since tanz/z is not a cardinal function, the "analogy" with the sinc ...

An analytic function f on the unit disk is called schlicht if 1. f is one-to-one, 2. f(0)=0, and 3. f^'(0)=1, in which case it is written f in S. Schlicht functions have ...

A function which has infinitely many derivatives at a point. If a function is not polygenic, it is monogenic.

The apodization function f(x)=1-(|x|)/a (1) which is a generalization of the one-argument triangle function. Its full width at half maximum is a. It has instrument function ...

If f is continuous on a closed interval [a,b], then there is at least one number x^* in [a,b] such that int_a^bf(x)dx=f(x^*)(b-a). The average value of the function (f^_) on ...

A function f(t) of one or more parameters containing a noise term epsilon(t) f(t)=L(t)+epsilon(t), where the noise is (without loss of generality) assumed to be additive.

Given a random variable X with continuous and strictly monotonic probability density function f(X), a quantile function Q_f assigns to each probability p attained by f the ...

An algebraic function is a function f(x) which satisfies p(x,f(x))=0, where p(x,y) is a polynomial in x and y with integer coefficients. Functions that can be constructed ...

A function f(x) is said to be periodic (or, when emphasizing the presence of a single period instead of multiple periods, singly periodic) with period p if f(x)=f(x+np) for ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...