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The first singular value k_1 of the elliptic integral of the first kind K(k), corresponding to K^'(k_1)=K(k_1), (1) is given by k_1 = 1/(sqrt(2)) (2) k_1^' = 1/(sqrt(2)). (3) ...

The Struve function, denoted H_n(z) or occasionally H_n(z), is defined as H_nu(z)=(1/2z)^(nu+1)sum_(k=0)^infty((-1)^k(1/2z)^(2k))/(Gamma(k+3/2)Gamma(k+nu+3/2)), (1) where ...

For a discrete function f(n), the summatory function is defined by F(n)=sum_(k in D)^nf(k), where D is the domain of the function.

When the elliptic modulus k has a singular value, the complete elliptic integrals may be computed in analytic form in terms of gamma functions. Abel (quoted in Whittaker and ...

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; ...

A function whose range is in the complex numbers is said to be a complex function, or a complex-valued function.

A special function mostly commonly denoted psi_n(z), psi^((n))(z), or F_n(z-1) which is given by the (n+1)st derivative of the logarithm of the gamma function Gamma(z) (or, ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

A convex function is a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the ...

There are two definitions of the Carmichael function. One is the reduced totient function (also called the least universal exponent function), defined as the smallest integer ...