DLMF:4.23.E40 (Q1792)

From DRMF

Revision as of 18:36, 1 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Jump to navigation Jump to search

No description defined

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).}}

0 references

DLMF:4.23.E40

0 references

Gudermannian function

Defining formula

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

C4.S23.E39.m2aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2andec

0 references

base of natural logarithm

Defining formula

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

C4.S2.E11.m2adec

0 references

hyperbolic cosecant function

Defining formula

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

C4.S28.E5.m2adec

0 references

hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2adec

0 references

hyperbolic cotangent function

Defining formula

{\displaystyle{\displaystyle\coth\NVar{z}}}

C4.S28.E7.m2adec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q1792&oldid=27566"