Lommel polynomial explained
\displaystyleJm+\nu(z)=J\nu(z)Rm,\nu(z)-J\nu-1(z)Rm-1,\nu+1(z)
where
Jν(
z) is a
Bessel function of the first kind.
[1] They are given explicitly by
Rm,\nu(z)=
| (-1)n(m-n)!\Gamma(\nu+m-n) |
n!(m-2n)!\Gamma(\nu+n) |
(z/2)2n-m.
See also
Notes and References
- . 1871 . Zur Theorie der Bessel'schen Functionen . Mathematische Annalen . 4 . 1 . 103–116 . Springer . Berlin / Heidelberg . 10.1007/BF01443302.