Digital Library of Mathematical Functions
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10 Bessel FunctionsKelvin Functions

§10.64 Integral Representations

Schläfli-Type Integrals

10.64.1 bern(x2)=(-1)nπ0πcos(xsint-nt)cosh(xsint)t,
10.64.2 bein(x2)=(-1)nπ0πsin(xsint-nt)sinh(xsint)t.

See Apelblat (1991) for these results, and also for similar representations for berν(x2), beiν(x2), and their ν-derivatives.