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10 Bessel FunctionsSpherical Bessel Functions

§10.56 Generating Functions

When 2|t|<|z|,

10.56.1 cosz22ztz =coszz+n=1tnn!𝗃n1(z),
10.56.2 sinz22ztz =sinzz+n=1tnn!𝗒n1(z).
10.56.3 coshz2+2iztz =coshzz+n=1(it)nn!𝗂n1(1)(z),
10.56.4 sinhz2+2iztz =sinhzz+n=1(it)nn!𝗂n1(2)(z),
10.56.5 exp(z2+2izt)z=ezz+2πn=1(it)nn!𝗄n1(z).