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S(nu,z) = int_0^infty(1+t)^(-nu)e^(-zt)dt (1) = z^(nu-1)e^zint_z^inftyu^(-nu)e^(-u)du (2) = z^(nu/2-1)e^(z/2)W_(-nu/2,(1-nu)/2)(z), (3) where W_(k,m)(z) is the Whittaker ...

The exponential sum function e_n(x), sometimes also denoted exp_n(x), is defined by e_n(x) = sum_(k=0)^(n)(x^k)/(k!) (1) = (e^xGamma(n+1,x))/(Gamma(n+1)), (2) where ...

The function f(x,y)=(1-x)^2+100(y-x^2)^2 that is often used as a test problem for optimization algorithms (where a variation with 100 replaced by 105 is sometimes used; ...

The Mertens function is the summary function M(n)=sum_(k=1)^nmu(k), (1) where mu(n) is the Möbius function (Mertens 1897; Havil 2003, p. 208). The first few values are 1, 0, ...

A cadlag function is a function, defined on R or a subset of R, that is right continuous and has a left limit. The acronym cadlag comes from the French "continue à droite, ...

f(I) is the collection of all real-valued continuous functions defined on some interval I. f^((n))(I) is the collection of all functions in f(I) with continuous nth ...

The function giving the volume of the spherical quadrectangular tetrahedron: V=(pi^2)/8f(pi/p,pi/q,pi/r), (1) where (2) and D=sqrt(cos^2xcos^2z-cos^2y). (3)

For any alpha in A (where A denotes the set of algebraic numbers), let |alpha|^_ denote the maximum of moduli of all conjugates of alpha. Then a function ...

A hash function H projects a value from a set with many (or even an infinite number of) members to a value from a set with a fixed number of (fewer) members. Hash functions ...

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 ...