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A radial function is a function phi:R^+->R satisfying phi(x,c)=phi(|x-c|) for points c in some subset Xi subset R^n. Here, |·| denotes the standard Euclidean norm in R^n and ...

For a power function f(x)=x^k with k>=0 on the interval [0,2L] and periodic with period 2L, the coefficients of the Fourier series are given by a_0 = (2^(k+1)L^k)/(k+1) (1) ...

The function defined by the contour integral J_(n,k)(z) =1/(2pii)int^((0+))t^(-n-1)(t+1/t)^kexp[1/2z(t-1/t)]dt, where int_((0+)) denotes the contour encircling the point z=0 ...

Given a hypergeometric or generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;z), the corresponding regularized hypergeometric function is defined by where ...

The "natural exponential function" is the name sometimes given in elementary contexts to the function f(x)=e^x, where e =2.718... is the base of the natural logarithm. While ...

Informally, a function f:{0,1}^(l(n))×{0,1}^n->{0,1}^(m(n)) is a trapdoor one-way function if 1. It is a one-way function, and 2. For fixed public key y in {0,1}^(l(n)), ...

Landau's function g(n) is the maximum order of an element in the symmetric group S_n. The value g(n) is given by the largest least common multiple of all partitions of the ...

The apodization function A(x)=cos((pix)/(2a)). Its full width at half maximum is 4a/3. Its instrument function is I(k)=(4acos(2piak))/(pi(1-16a^2k^2)), which has a maximum of ...

If Li_2(x) denotes the usual dilogarithm, then there are two variants that are normalized slightly differently, both called the Rogers L-function (Rogers 1907). Bytsko (1999) ...

The pseudosmarandache function Z(n) is the smallest integer such that sum_(k=1)^(Z(n))k=1/2Z(n)[Z(n)+1] is divisible by n. The values for n=1, 2, ... are 1, 3, 2, 7, 4, 3, 6, ...