表达式
双曲函数
\(\operatorname{sh} x = \dfrac{e^{x}-e^{-x}}{2}\)
\(\operatorname{ch} x = \dfrac{e^{x}+e^{-x}}{2}\)
\(\operatorname{th} x = \dfrac{e^{x}-e^{-x}}{e^{x}+e^{-x}}\)
\(\operatorname{cth} x = \dfrac{e^{x}+e^{-x}}{e^{x}-e^{-x}}\)
\(\operatorname{sech} x = \dfrac{2}{e^{x}+e^{-x}}\)
\(\operatorname{csch} x = \dfrac{2}{e^{x}-e^{-x}}\)
反双曲函数
\(\operatorname{arsinh} x = \ln {(x+\sqrt{x^2+1})}\)
\(\operatorname{arcosh} x = \ln {(x+\sqrt{x^2-1})}\)
\(\operatorname{artanh} x = \dfrac{1}{2} \ln {\dfrac{1+x}{1-x}}\)
\(\operatorname{arcoth} x = \dfrac{1}{2} \ln {\dfrac{x+1}{x-1}}\)
\(\operatorname{arsech} x = \ln {(\dfrac{1}{x}+\sqrt{\dfrac{1}{x^2}-1})}\)
\(\operatorname{arcsch} x = \ln {(\dfrac{1}{x}+\sqrt{\dfrac{1}{x^2}+1})}\)
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