Lommel Polynomial

$R_{m,\nu}(z) ={\Gamma(\nu+m)\over\Gamma(\nu)(z/2)^m} \,{}_2F_3({\textstyle{1\over 2}}(1-m), -{\textstyle{1\over 2}}m; \nu, -m, 1-\nu-m; z^2)$

$\times {\pi z\over 2\sin(\nu\pi)}[J_{\nu+m}(z)J_{-\nu+1}(z) +(-1)^mJ_{-\nu-m}(z)J_{\nu-1}(z)],$

where $\Gamma(z)$ is a Gamma Function, is a Bessel Function of the First Kind, and ${}_2F_3(a,b;c,d,e;z)$ is a Generalized Hypergeometric Function.

See also Lommel Function

References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1477, 1980.

$R_{m,\nu}(z) ={\Gamma(\nu+m)\over\Gamma(\nu)(z/2)^m} \,{}_2F_3({\textstyle{1\over 2}}(1-m), -{\textstyle{1\over 2}}m; \nu, -m, 1-\nu-m; z^2)$
$\times {\pi z\over 2\sin(\nu\pi)}[J_{\nu+m}(z)J_{-\nu+1}(z) +(-1)^mJ_{-\nu-m}(z)J_{\nu-1}(z)],$