Digital Library of Mathematical Functions
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NIST
4 Elementary FunctionsHyperbolic Functions

§4.36 Infinite Products and Partial Fractions

4.36.1 sinhz =zn=1(1+z2n2π2),
4.36.2 coshz =n=1(1+4z2(2n-1)2π2).

When znπ, n,

4.36.3 cothz =1z+2zn=11z2+n2π2,
4.36.4 csch2z =n=-1(z-nπ)2,
4.36.5 cschz =1z+2zn=1(-1)nz2+n2π2.