Search Results for ""

The Kampé de Fériet function is a special function that generalizes the generalized hypergeometric function to two variables and includes the Appell hypergeometric function ...

Odd values of Q(n) are 1, 1, 3, 5, 27, 89, 165, 585, ... (OEIS A051044), and occur with ever decreasing frequency as n becomes large (unlike P(n), for which the fraction of ...

A function f(x) is absolutely monotonic in the interval a<x<b if it has nonnegative derivatives of all orders in the region, i.e., f^((k))(x)>=0 (1) for a<x<b and k=0, 1, 2, ...

The confluent hypergeometric function of the second kind gives the second linearly independent solution to the confluent hypergeometric differential equation. It is also ...

Zeros of the Riemann zeta function zeta(s) come in two different types. So-called "trivial zeros" occur at all negative even integers s=-2, -4, -6, ..., and "nontrivial ...

rho_(2s)(n)=(pi^s)/(Gamma(s))n^(s-1)sum_(p,q)((S_(p,q))/q)^(2s)e^(2nppii/q), where S_(p,q) is a Gaussian sum, and Gamma(s) is the gamma function.

Levenberg-Marquardt is a popular alternative to the Gauss-Newton method of finding the minimum of a function F(x) that is a sum of squares of nonlinear functions, ...

Let R(x) be the ramp function, then the Fourier transform of R(x) is given by F_x[R(x)](k) = int_(-infty)^inftye^(-2piikx)R(x)dx (1) = i/(4pi)delta^'(k)-1/(4pi^2k^2), (2) ...

For R[nu]>-1/2, J_nu(z)=(z/2)^nu2/(sqrt(pi)Gamma(nu+1/2))int_0^(pi/2)cos(zcost)sin^(2nu)tdt, where J_nu(z) is a Bessel function of the first kind, and Gamma(z) is the gamma ...

The spherical Bessel function of the second kind, denoted y_nu(z) or n_nu(z), is defined by y_nu(z)=sqrt(pi/(2z))Y_(nu+1/2)(z), (1) where Y_nu(z) is a Bessel function of the ...