Lommel polynomial

Short description: Concept in mathematics

A Lommel polynomial Rm,ν(z) is a polynomial in 1/z giving the recurrence relation

Jm+ν(z)=Jν(z)Rm,ν(z)−Jν−1(z)Rm−1,ν+1(z)

where Jν(z) is a Bessel function of the first kind.[1]

They are given explicitly by

Rm,ν(z)=∑n=0[m/2](−1)n(m−n)!Γ(ν+m−n)n!(m−2n)!Γ(ν+n)(z/2)2n−m.

## See also

* Lommel function
* Neumann polynomial

## References

1. ↑ Eugen von Lommel (1871). "Zur Theorie der Bessel'schen Functionen". Mathematische Annalen (Berlin / Heidelberg: Springer) 4 (1): 103–116. doi:10.1007/BF01443302.

* Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G. (1953), Higher transcendental functions. Vol II, McGraw-Hill Book Company, Inc., New York-Toronto-London, http://apps.nrbook.com/bateman/Vol2.pdf
* Hazewinkel, Michiel, ed. (2001), "l/l060810", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=l/l060810

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