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Showing content from https://dlmf.nist.gov/4.30 below:

§4.30 Elementary Properties ‣ Hyperbolic Functions ‣ Chapter 4 Elementary Functions

sinh ⁡ θ a ( a2 − 1 ) 1 / 2 a ⁢ ( 1 − a2 ) − 1 / 2 a − 1 a − 1 ⁢ ( 1 − a2 ) 1 / 2 ( a2 − 1 ) − 1 / 2 cosh ⁡ θ ( 1 + a2 ) 1 / 2 a ( 1 − a2 ) − 1 / 2 a − 1 ⁢ ( 1 + a2 ) 1 / 2 a − 1 a ⁢ ( a2 − 1 ) − 1 / 2 tanh ⁡ θ a ⁢ ( 1 + a2 ) − 1 / 2 a − 1 ⁢ ( a2 − 1 ) 1 / 2 a ( 1 + a2 ) − 1 / 2 ( 1 − a2 ) 1 / 2 a − 1 csch ⁡ θ a − 1 ( a2 − 1 ) − 1 / 2 a − 1 ⁢ ( 1 − a2 ) 1 / 2 a a ⁢ ( 1 − a2 ) − 1 / 2 ( a2 − 1 ) 1 / 2 sech ⁡ θ ( 1 + a2 ) − 1 / 2 a − 1 ( 1 − a2 ) 1 / 2 a ⁢ ( 1 + a2 ) − 1 / 2 a a − 1 ⁢ ( a2 − 1 ) 1 / 2 coth ⁡ θ a − 1 ⁢ ( a2 + 1 ) 1 / 2 a ⁢ ( a2 − 1 ) − 1 / 2 a − 1 ( 1 + a2 ) 1 / 2 ( 1 − a2 ) − 1 / 2 a

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