Lommel Polynomial
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A Lommel polynomial ''R''''m'',ν(''z'') is a polynomial in 1/''z'' giving the
recurrence relation In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter ...
:\displaystyle J_(z) = J_\nu(z)R_(z) - J_(z)R_(z) where ''J''ν(''z'') is a
Bessel function Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex ...
of the first kind. They are given explicitly by :R_(z) = \sum_^\frac(z/2)^.


See also

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Lommel function Lommel () is a Municipalities of Belgium, municipality and City status in Belgium, city in the Belgium, Belgian province of Limburg (Belgium), Limburg. Lying in the Campine, Kempen, it has about 34,000 inhabitants and is part of the arrondissement ...
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Neumann polynomial In mathematics, the Neumann polynomials, introduced by Carl Neumann for the special case \alpha=0, are a sequence of polynomials in 1/t used to expand functions in term of Bessel functions. The first few polynomials are :O_0^(t)=\frac 1 t, :O_1^(t) ...


References

* * Polynomials Special functions {{polynomial-stub