- Lommel polynomial
A Lommel polynomial "R""m",ν("z"), introduced by harvs|txt|authorlink=Eugen von Lommel|first=Eugen von|last= Lommel|year=1871, is a polynomial in 1/"z" giving the recurrence relation :displaystyle J_{m+ u}(z) = J_ u(z)R_{m, u}(z) - J_{ u-1}(z)R_{m-1, u+1}(z) where "J"ν("z") is a
Bessel function of the first kind.They are given explicitly by:R_{m, u} = sum_{n=0}^{ [m/2] }frac{(-1)^m(m-n)!Gamma( u+m-n)}{n!(m-2n)!Gamma( u+n)}(z/2)^{2n-m}.
ee also
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Lommel function References
*Citation | last1=Erdélyi | first1=Arthur | author-link=Arthur Erdélyi | last2=Magnus | first2=Wilhelm | author2-link=Wilhelm Magnus | last3=Oberhettinger | first3=Fritz | last4=Tricomi | first4=Francesco G. | title=Higher transcendental functions. Vol II | publisher=McGraw-Hill Book Company, Inc., New York-Toronto-London | id=MathSciNet | id = 0058756 | year=1953
*springer|id=l/l060810|first=A. B. |last=Ivanov
*citation|first=Eugen von |last=Lommel|title=Zur Theorie der Bessel'schen Functionen
journal =Mathematische Annalen
publisher =Springer |place=Berlin / Heidelberg
ISSN=1432-1807
volume =4|issue= 1 |year= 1871
DOI =10.1007/BF01443302
pages =103-116
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