DLMF:22.16.E8 (Q7127): Difference between revisions

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Revision as of 15:31, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:22.16.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{am}\left(x,k\right)=\operatorname{gd% }x-\tfrac{1}{4}{k^{\prime}}^{2}(x-\sinh x\cosh x)\operatorname{sech}x+O\left({% k^{\prime}}^{4}\right).}}

0 references

DLMF:22.16.E8

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2abdec

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Gudermannian function

Defining formula

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

C4.S23.E39.m2aadec

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Jacobi’s amplitude function

Defining formula

{\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}

C22.S16.E1.m2agdec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2adec

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hyperbolic secant function

Defining formula

{\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}

C4.S28.E6.m2adec

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hyperbolic sine function

Defining formula

{\displaystyle{\displaystyle\sinh\NVar{z}}}

C4.S28.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle x}}

C22.S1.XMD1.m1gdec

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Sitelinks

Wikipedia(0 entries)

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