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10 Bessel FunctionsSpherical Bessel Functions

§10.53 Power Series

10.53.1 𝗃n(z)=znk=0(12z2)kk!(2n+2k+1)!!,
10.53.2 𝗒n(z)=1zn+1k=0n(2n2k1)!!(12z2)kk!+(1)n+1zn+1k=n+1(12z2)kk!(2k2n1)!!.
10.53.3 𝗂n(1)(z) =znk=0(12z2)kk!(2n+2k+1)!!,
10.53.4 𝗂n(2)(z) =(1)nzn+1k=0n(2n2k1)!!(12z2)kk!+1zn+1k=n+1(12z2)kk!(2k2n1)!!.

For 𝗁n(1)(z) and 𝗁n(2)(z) combine (10.47.10), (10.53.1), and (10.53.2). For 𝗄n(z) combine (10.47.11), (10.53.3), and (10.53.4).