Lommel polynomial

A Lommel polynomial R^m,ν(z), introduced by Eugen von Lommel (1871), is a polynomial in 1/z giving the recurrence relation

where J_ν(z) is a Bessel function of the first kind.

They are given explicitly by

See also

* Lommel function
* Neumann polynomial

References

* Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G. (1953), Higher transcendental functions. Vol II, McGraw-Hill Book Company, Inc., New York-Toronto-London, MR0058756
* Ivanov, A. B. (2001), "Lommel polynomial", in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Springer, ISBN 978-1556080104, http://eom.springer.de/l/l060810.htm
* Lommel, Eugen von (1871), "Zur Theorie der Bessel'schen Functionen", Mathematische Annalen (Berlin / Heidelberg: Springer) 4 (1): 103–116, doi:10.1007/BF01443302