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There are two types of functions known as Hankel functions. The more common one is a complex function (also called a Bessel function of the third kind, or Weber Function) ...

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 ...

A quotient of two polynomials P(z) and Q(z), R(z)=(P(z))/(Q(z)), is called a rational function, or sometimes a rational polynomial function. More generally, if P and Q are ...

The sum of powers of even divisors of a number. It is the analog of the divisor function for even divisors only and is written sigma_k^((e))(n). It is given simply in terms ...

A simple function is a finite sum sum_(i)a_ichi_(A_i), where the functions chi_(A_i) are characteristic functions on a set A. Another description of a simple function is a ...

The finite Fourier cosine transform of an apodization function, also known as an apparatus function. The instrument function I(k) corresponding to a given apodization ...

An arithmetic function is a function f(n) defined for all n in N, usually taken to be complex-valued, so that f:N->C (Jones and Jones 1998, p. 143). An alternative definition ...

A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) ...

A function f in C^infty(R^n) is called a Schwartz function if it goes to zero as |x|->infty faster than any inverse power of x, as do all its derivatives. That is, a function ...

An analytic function f(z) satisfying the irreducible algebraic equation A_0(z)f^k+A_1(z)f^(k-1)+...+A_k(z)=0 with single-valued meromorphic functions A_j(z) in a complex ...