Search Results for ""

For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. ...

A unimodular matrix is a real square matrix A with determinant det(A)=+/-1 (Born and Wolf 1980, p. 55; Goldstein 1980, p. 149). More generally, a matrix A with elements in ...

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) ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

The Jacobi polynomials, also known as hypergeometric polynomials, occur in the study of rotation groups and in the solution to the equations of motion of the symmetric top. ...

The Gegenbauer polynomials C_n^((lambda))(x) are solutions to the Gegenbauer differential equation for integer n. They are generalizations of the associated Legendre ...

An indicial equation, also called a characteristic equation, is a recurrence equation obtained during application of the Frobenius method of solving a second-order ordinary ...

A star polygon {p/q}, with p,q positive integers, is a figure formed by connecting with straight lines every qth point out of p regularly spaced points lying on a ...

Solutions to the associated Laguerre differential equation with nu!=0 and k an integer are called associated Laguerre polynomials L_n^k(x) (Arfken 1985, p. 726) or, in older ...

The W polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. (The corresponding w polynomials are called Lucas polynomials.) They have explicit ...