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The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, ...

(theta_3(z,t)theta_4(z,t))/(theta_4(2z,2t))=(theta_3(0,t)theta_4(0,t))/(theta_4(0,2t))=(theta_2(z,t)theta_1(z,t))/(theta_1(2z,2t)), where theta_i are Jacobi theta functions. ...

Lauricella functions are generalizations of the Gauss hypergeometric functions to multiple variables. Four such generalizations were investigated by Lauricella (1893), and ...

Every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement ...

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, ...

One of the quantities lambda_i appearing in the Gauss-Jacobi mechanical quadrature. They satisfy lambda_1+lambda_2+...+lambda_n = int_a^bdalpha(x) (1) = alpha(b)-alpha(a) (2) ...

Stationary iterative methods are methods for solving a linear system of equations Ax=b, where A is a given matrix and b is a given vector. Stationary iterative methods can be ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

65537 is the largest known Fermat prime, and the 65537-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. The 65537-gon has so many ...

A Gaussian sum is a sum of the form S(p,q)=sum_(r=0)^(q-1)e^(-piir^2p/q), (1) where p and q are relatively prime integers. The symbol phi is sometimes used instead of S. ...