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mathematical physics > special function > Lommel polynomial

mathematical analysis > functional analysis > special function > Lommel polynomial

mathematical analysis > function > elementary function > polynomial > Lommel polynomial

algebra > polynomial > Lommel polynomial

Terme préférentiel

Lommel polynomial

Définition(s)

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

${\\displaystyle \\displaystyle J_{m+\ u }(z)=J_{\ u }(z)R_{m,\ u }(z)-J_{\ u -1}(z)R_{m-1,\ u +1}(z)}$

where J_ν(z) is a Bessel function of the first kind.
They are given explicitly by

${\\displaystyle R_{m,\ u }(z)=\\sum _{n=0}^{[m/2]}{\ rac {(-1)^{n}(m-n)!\\Gamma (\ u +m-n)}{n!(m-2n)!\\Gamma (\ u +n)}}(z/2)^{2n-m}.}$

Concept(s) générique(s)

Traductions

polynôme de Lommel

français

URI

http://data.loterre.fr/ark:/67375/PSR-ZD1X01FM-W

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RDF/XML TURTLE JSON-LD Date de création 16/08/2023, dernière modif. 16/08/2023