Search Results for ""

An apodization function similar to the Bartlett function.

The Barnes G-function is an analytic continuation of the G-function defined in the construction of the Glaisher-Kinkelin constant G(n)=([Gamma(n)]^(n-1))/(H(n-1)) (1) for ...

A function that has a natural boundary.

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

A pairing function is a function that reversibly maps Z^*×Z^* onto Z^*, where Z^*={0,1,2,...} denotes nonnegative integers. Pairing functions arise naturally in the ...

A function which is not an algebraic function. In other words, a function which "transcends," i.e., cannot be expressed in terms of, algebra. Examples of transcendental ...

An entire function which is a generalization of the Bessel function of the first kind defined by J_nu(z)=1/piint_0^picos(nutheta-zsintheta)dtheta. Anger's original function ...

The function Pi_(a,b)(x)=H(x-a)-H(x-b) which is equal to 1 for a<=x<=b and 0 otherwise. Here H(x) is the Heaviside step function. The special case Pi_(-1/2,1/2)(x) gives the ...