Elementary Functions - 4.28 Definitions and Periodicity

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
4.28.E1	${\displaystyle{\displaystyle\sinh z=\frac{e^{z}-e^{-z}}{2}}}$ \sinh@@{z} = \frac{e^{z}-e^{-z}}{2}		sinh(z) = (exp(z)- exp(- z))/(2)	Sinh[z] == Divide[Exp[z]- Exp[- z],2]	Successful	Successful	-	Successful [Tested: 7]
4.28.E2	${\displaystyle{\displaystyle\cosh z=\frac{e^{z}+e^{-z}}{2}}}$ \cosh@@{z} = \frac{e^{z}+e^{-z}}{2}		cosh(z) = (exp(z)+ exp(- z))/(2)	Cosh[z] == Divide[Exp[z]+ Exp[- z],2]	Successful	Successful	-	Successful [Tested: 7]
4.28.E3	${\displaystyle{\displaystyle\cosh z+\sinh z=e^{+z}}}$ \cosh@@{z}+\sinh@@{z} = e^{+ z}		cosh(z)+ sinh(z) = exp(+ z)	Cosh[z]+ Sinh[z] == Exp[+ z]	Successful	Successful	-	Successful [Tested: 7]
4.28.E3	${\displaystyle{\displaystyle\cosh z-\sinh z=e^{-z}}}$ \cosh@@{z}-\sinh@@{z} = e^{- z}		cosh(z)- sinh(z) = exp(- z)	Cosh[z]- Sinh[z] == Exp[- z]	Successful	Successful	-	Successful [Tested: 7]
4.28.E4	${\displaystyle{\displaystyle\tanh z=\frac{\sinh z}{\cosh z}}}$ \tanh@@{z} = \frac{\sinh@@{z}}{\cosh@@{z}}		tanh(z) = (sinh(z))/(cosh(z))	Tanh[z] == Divide[Sinh[z],Cosh[z]]	Successful	Successful	-	Successful [Tested: 7]
4.28.E5	${\displaystyle{\displaystyle\operatorname{csch}z=\frac{1}{\sinh z}}}$ \csch@@{z} = \frac{1}{\sinh@@{z}}		csch(z) = (1)/(sinh(z))	Csch[z] == Divide[1,Sinh[z]]	Successful	Successful	-	Successful [Tested: 7]
4.28.E6	${\displaystyle{\displaystyle\operatorname{sech}z=\frac{1}{\cosh z}}}$ \sech@@{z} = \frac{1}{\cosh@@{z}}		sech(z) = (1)/(cosh(z))	Sech[z] == Divide[1,Cosh[z]]	Successful	Successful	-	Successful [Tested: 7]
4.28.E7	${\displaystyle{\displaystyle\coth z=\frac{1}{\tanh z}}}$ \coth@@{z} = \frac{1}{\tanh@@{z}}		coth(z) = (1)/(tanh(z))	Coth[z] == Divide[1,Tanh[z]]	Successful	Successful	-	Successful [Tested: 7]
4.28.E8	${\displaystyle{\displaystyle\sin\left(iz\right)=i\sinh z}}$ \sin@{iz} = i\sinh@@{z}		sin(I*z) = I*sinh(z)	Sin[I*z] == I*Sinh[z]	Successful	Successful	-	Successful [Tested: 7]
4.28.E9	${\displaystyle{\displaystyle\cos\left(iz\right)=\cosh z}}$ \cos@{iz} = \cosh@@{z}		cos(I*z) = cosh(z)	Cos[I*z] == Cosh[z]	Successful	Successful	-	Successful [Tested: 7]
4.28.E10	${\displaystyle{\displaystyle\tan\left(iz\right)=i\tanh z}}$ \tan@{iz} = i\tanh@@{z}		tan(I*z) = I*tanh(z)	Tan[I*z] == I*Tanh[z]	Successful	Successful	-	Successful [Tested: 7]
4.28.E11	${\displaystyle{\displaystyle\csc\left(iz\right)=-i\operatorname{csch}z}}$ \csc@{iz} = -i\csch@@{z}		csc(I*z) = - I*csch(z)	Csc[I*z] == - I*Csch[z]	Successful	Successful	-	Successful [Tested: 7]
4.28.E12	${\displaystyle{\displaystyle\sec\left(iz\right)=\operatorname{sech}z}}$ \sec@{iz} = \sech@@{z}		sec(I*z) = sech(z)	Sec[I*z] == Sech[z]	Successful	Successful	-	Successful [Tested: 7]
4.28.E13	${\displaystyle{\displaystyle\cot\left(iz\right)=-i\coth z}}$ \cot@{iz} = -i\coth@@{z}		cot(I*z) = - I*coth(z)	Cot[I*z] == - I*Coth[z]	Successful	Successful	-	Successful [Tested: 7]