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10 Bessel FunctionsKelvin Functions

§10.66 Expansions in Series of Bessel Functions

10.66.1 berνx+ibeiνx=k=0e(3ν+k)πi/4xkJν+k(x)2k/2k!=k=0e(3ν+3k)πi/4xkIν+k(x)2k/2k!.
10.66.2 bern(x2) =k=-(-1)n+kJn+2k(x)I2k(x),
bein(x2) =k=-(-1)n+kJn+2k+1(x)I2k+1(x).