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

Revision as of 18:36, 1 January 2020

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

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

C4.S23.E39.m2aadec

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@@ Property / Symbols used @@
+Gudermannian function
@@ Property / Symbols used: Gudermannian function / rank @@
+Normal rank
@@ Property / Symbols used: Gudermannian function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\operatorname{gd}\NVar{x}}}$ 
\Gudermannian@@{\NVar{x}}
@@ Property / Symbols used: Gudermannian function / qualifier @@
+xml-id: C4.S23.E39.m2aadec