DLMF:4.23.E40 (Q1792): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:4.23.E40	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{gd}\left(x\right)=2\operatorname{% arctan}\left(e^{x}\right)-\tfrac{1}{2}\pi\\ =\operatorname{arcsin}\left(\tanh x\right)=\operatorname{arccsc}\left(\coth x% \right)\\ =\operatorname{arccos}\left(\operatorname{sech}x\right)=\operatorname{arcsec}% \left(\cosh x\right)\\ =\operatorname{arctan}\left(\sinh x\right)=\operatorname{arccot}\left(% \operatorname{csch}x\right).}}

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DLMF:4.23.E40

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Gudermannian function

Defining formula

{\displaystyle{\displaystyle\operatorname{gd}\NVar{x}}}

C4.S23.E39.m2aadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2andec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2adec

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hyperbolic cosecant function

Defining formula

{\displaystyle{\displaystyle\operatorname{csch}\NVar{z}}}

C4.S28.E5.m2adec

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hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2adec

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Sitelinks

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