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Let A be a set. An operation on A is a function from a power of A into A. More precisely, given an ordinal number alpha, a function from A^alpha into A is an alpha-ary ...

Let f be a function defined on a set A and taking values in a set B. Then f is said to be a surjection (or surjective map) if, for any b in B, there exists an a in A for ...

An apodization function, also called the Hann function, frequently used to reduce leakage in discrete Fourier transforms. The illustrations above show the Hanning function, ...

The apodization function A(x)=1-(x^2)/(a^2). (1) Its full width at half maximum is sqrt(2)a. Its instrument function is I(k) = 2asqrt(2pi)(J_(3/2)(2pika))/((2pika)^(3/2)) (2) ...

By analogy with the tanc function, define the tanhc function by tanhc(z)={(tanhz)/z for z!=0; 1 for z=0. (1) It has derivative (dtanhc(z))/(dz)=(sech^2z)/z-(tanhz)/(z^2). (2) ...

The hyperfactorial (Sloane and Plouffe 1995) is the function defined by H(n) = K(n+1) (1) = product_(k=1)^(n)k^k, (2) where K(n) is the K-function. The hyperfactorial is ...

A knot invariant is a function from the set of all knots to any other set such that the function does not change as the knot is changed (up to isotopy). In other words, a ...

The spherical Hankel function of the first kind h_n^((1))(z) is defined by h_n^((1))(z) = sqrt(pi/(2z))H_(n+1/2)^((1))(z) (1) = j_n(z)+in_n(z), (2) where H_n^((1))(z) is the ...

A convolution is an integral that expresses the amount of overlap of one function g as it is shifted over another function f. It therefore "blends" one function with another. ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...