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The Lommel polynomials R_(m,nu)(z) arise from the equation J_(m+nu)(z)=J_nu(z)R_(m,nu)(z)-J_(nu-1)(z)R_(m-1,nu+1)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

There are several functions called "Lommel functions." One type of Lommel function appear in the solution to the Lommel differential equation and are given by ...

The Lommel differential equation is a generalization of the Bessel differential equation given by z^2y^('')+zy^'+(z^2-nu^2)y=kz^(mu+1), (1) or, in the most general form, by ...

The modified Lommel functions of the first and second kind give the solution to the Lommel differential equation with a minus sign in front of the linear term, i.e., ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

The two integrals involving Bessel functions of the first kind given by (alpha^2-beta^2)intxJ_n(alphax)J_n(betax)dx ...

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, ...

A rational polynomial is a polynomial having rational coefficients. While the term "rational polynomial" is sometimes used as a synonym for rational function, this usage is ...

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.