Elementary Functions - 4.28 Definitions and Periodicity
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 4.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{z} = \frac{e^{z}-e^{-z}}{2}}
\sinh@@{z} = \frac{e^{z}-e^{-z}}{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sinh(z) = (exp(z)- exp(- z))/(2)
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Sinh[z] == Divide[Exp[z]- Exp[- z],2]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z} = \frac{e^{z}+e^{-z}}{2}}
\cosh@@{z} = \frac{e^{z}+e^{-z}}{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cosh(z) = (exp(z)+ exp(- z))/(2)
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Cosh[z] == Divide[Exp[z]+ Exp[- z],2]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z}+\sinh@@{z} = e^{+ z}}
\cosh@@{z}+\sinh@@{z} = e^{+ z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cosh(z)+ sinh(z) = exp(+ z)
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Cosh[z]+ Sinh[z] == Exp[+ z]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z}-\sinh@@{z} = e^{- z}}
\cosh@@{z}-\sinh@@{z} = e^{- z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cosh(z)- sinh(z) = exp(- z)
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Cosh[z]- Sinh[z] == Exp[- z]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{z} = \frac{\sinh@@{z}}{\cosh@@{z}}}
\tanh@@{z} = \frac{\sinh@@{z}}{\cosh@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tanh(z) = (sinh(z))/(cosh(z))
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Tanh[z] == Divide[Sinh[z],Cosh[z]]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csch@@{z} = \frac{1}{\sinh@@{z}}}
\csch@@{z} = \frac{1}{\sinh@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | csch(z) = (1)/(sinh(z))
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Csch[z] == Divide[1,Sinh[z]]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sech@@{z} = \frac{1}{\cosh@@{z}}}
\sech@@{z} = \frac{1}{\cosh@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sech(z) = (1)/(cosh(z))
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Sech[z] == Divide[1,Cosh[z]]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coth@@{z} = \frac{1}{\tanh@@{z}}}
\coth@@{z} = \frac{1}{\tanh@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | coth(z) = (1)/(tanh(z))
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Coth[z] == Divide[1,Tanh[z]]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{iz} = i\sinh@@{z}}
\sin@{iz} = i\sinh@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sin(I*z) = I*sinh(z)
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Sin[I*z] == I*Sinh[z]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{iz} = \cosh@@{z}}
\cos@{iz} = \cosh@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cos(I*z) = cosh(z)
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Cos[I*z] == Cosh[z]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{iz} = i\tanh@@{z}}
\tan@{iz} = i\tanh@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tan(I*z) = I*tanh(z)
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Tan[I*z] == I*Tanh[z]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csc@{iz} = -i\csch@@{z}}
\csc@{iz} = -i\csch@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | csc(I*z) = - I*csch(z)
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Csc[I*z] == - I*Csch[z]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@{iz} = \sech@@{z}}
\sec@{iz} = \sech@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sec(I*z) = sech(z)
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Sec[I*z] == Sech[z]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.28.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@{iz} = -i\coth@@{z}}
\cot@{iz} = -i\coth@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cot(I*z) = - I*coth(z)
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Cot[I*z] == - I*Coth[z]
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Successful | Successful | - | Successful [Tested: 7] |