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A polynomial function of the elements of a vector x can be uniquely decomposed into a sum of harmonic polynomials times powers of |x|.

The function K_n(x_0,x)=K_n(x,x_0)^_=K_n(x^_,x^__0) which is useful in the study of many polynomials.

The ring R[x] of polynomials in a variable x.

A sequence of polynomials p_i(x), for i=0, 1, 2, ..., where p_i(x) is exactly of degree i for all i.

A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...

The second knot polynomial discovered. Unlike the first-discovered Alexander polynomial, the Jones polynomial can sometimes distinguish handedness (as can its more powerful ...

An n×m matrix A^- is a 1-inverse of an m×n matrix A for which AA^-A=A. (1) The Moore-Penrose matrix inverse is a particular type of 1-inverse. A matrix equation Ax=b (2) has ...

A series is an infinite ordered set of terms combined together by the addition operator. The term "infinite series" is sometimes used to emphasize the fact that series ...

The Legendre polynomials, sometimes called Legendre functions of the first kind, Legendre coefficients, or zonal harmonics (Whittaker and Watson 1990, p. 302), are solutions ...

B(x,y)=[x y; +/-ty +/-x]. (1) It satisfies B(x_1,y_1)B(x_2,y_2)=B(x_1x_2+/-ty_1y_2,x_1y_2+/-y_1x_2). (2) Powers of the matrix are defined by B^n = [x y; ty x]^n (3) = [x_n ...