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

A 1-variable unoriented knot polynomial Q(x). It satisfies Q_(unknot)=1 (1) and the skein relationship Q_(L_+)+Q_(L_-)=x(Q_(L_0)+Q_(L_infty)). (2) It also satisfies ...

Let n be an integer such that n>=lambda_1, where lambda=(lambda_1,lambda_2,...) is a partition of n=|lambda| if lambda_1>=lambda_2>=...>=0, where lambda_i are a sequence of ...

The hypergeometric orthogonal polynomials defined by P_n^((lambda))(x;phi)=((2lambda)_n)/(n!)e^(inphi)_2F_1(-n,lambda+ix;2lambda;1-e^(-2iphi)), (1) where (x)_n is the ...

A knot invariant in the form of a polynomial such as the Alexander polynomial, BLM/Ho Polynomial, bracket polynomial, Conway polynomial, HOMFLY polynomial, Jones polynomial, ...

The remainder R(x) obtained when dividing a polynomial p(x) by another polynomial q(x). The polynomial remainder is implemented in the Wolfram Language as ...

A complex polynomial is a polynomial with complex coefficients.

A multivariate polynomial (i.e., a polynomial in more than one variable) with all terms having the same degree. For example, x^3+xyz+y^2z+z^3 is a homogeneous polynomial of ...

The bracket polynomial is one-variable knot polynomial related to the Jones polynomial. The bracket polynomial, however, is not a topological invariant, since it is changed ...

The quotient of two polynomials p(x) and q(x), discarding any polynomial remainder. Polynomial quotients are implemented in the Wolfram Language as PolynomialQuotient[p, q, ...