Digital Library of Mathematical Functions
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10 Bessel FunctionsBessel and Hankel Functions

§10.5 Wronskians and Cross-Products

10.5.1 𝒲{Jν(z),J-ν(z)}=Jν+1(z)J-ν(z)+Jν(z)J-ν-1(z)=-2sin(νπ)/(πz),
10.5.2 𝒲{Jν(z),Yν(z)}=Jν+1(z)Yν(z)-Jν(z)Yν+1(z)=2/(πz),
10.5.3 𝒲{Jν(z),Hν(1)(z)}=Jν+1(z)Hν(1)(z)-Jν(z)Hν+1(1)(z)=2/(πz),
10.5.4 𝒲{Jν(z),Hν(2)(z)}=Jν+1(z)Hν(2)(z)-Jν(z)Hν+1(2)(z)=-2/(πz),
10.5.5 𝒲{Hν(1)(z),Hν(2)(z)}=Hν+1(1)(z)Hν(2)(z)-Hν(1)(z)Hν+1(2)(z)=-4/(πz).