Lommel polynomial

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

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

They are given explicitly by

See also

References

  • Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G. (1953), Higher transcendental functions. Vol II (PDF), McGraw-Hill Book Company, Inc., New York-Toronto-London, MR 0058756
  • Ivanov, A. B. (2001) [1994], "Lommel polynomial", Encyclopedia of Mathematics, EMS Press
  • Lommel, Eugen von (1871), "Zur Theorie der Bessel'schen Functionen", Mathematische Annalen, Berlin / Heidelberg: Springer, 4 (1): 103–116, doi:10.1007/BF01443302
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