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A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in ...

Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by ...

Each double point assigned to an irreducible algebraic curve whose curve genus is nonnegative imposes exactly one condition.

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

Gamma functions of argument 2z can be expressed in terms of gamma functions of smaller arguments. From the definition of the beta function, ...

The function defined by chi_nu(z)=sum_(k=0)^infty(z^(2k+1))/((2k+1)^nu). (1) It is related to the polylogarithm by chi_nu(z) = 1/2[Li_nu(z)-Li_nu(-z)] (2) = ...

Legendre's formula counts the number of positive integers less than or equal to a number x which are not divisible by any of the first a primes, (1) where |_x_| is the floor ...

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, ...

An ordering for the Cartesian product × of any two sets A and B with order relations <A and <B, respectively, such that if (a_1,b_1) and (a_2,b_2) both belong to A×B, then ...

Line segment picking is the process of picking line segments at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a ...