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4 Elementary FunctionsHyperbolic Functions

§4.33 Maclaurin Series and Laurent Series

4.33.1 sinhz=z+z33!+z55!+,
4.33.2 coshz=1+z22!+z44!+.
4.33.3 tanhz=z-z33+215z5-17315z7++22n(22n-1)B2n(2n)!z2n-1+,
|z|<12π.

For B2n see §24.2(i). For expansions that correspond to (4.19.4)–(4.19.9), change z to iz and use (4.28.8)–(4.28.13).