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

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Revision as of 15:31, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:31, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			hyperbolic secant function
		Property / Symbols used: hyperbolic secant function / rank
			Normal rank
		Property / Symbols used: hyperbolic secant function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}$ \sech@@{\NVar{z}}
		Property / Symbols used: hyperbolic secant function / qualifier
			xml-id: C4.S28.E6.m2adec
		Property / Symbols used
			hyperbolic sine function
		Property / Symbols used: hyperbolic sine function / rank
			Normal rank
		Property / Symbols used: hyperbolic sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sinh\NVar{z}}}$ \sinh@@{\NVar{z}}
		Property / Symbols used: hyperbolic sine function / qualifier
			xml-id: C4.S28.E1.m2adec
		Property / Symbols used
			Q12003
		Property / Symbols used: Q12003 / rank
			Normal rank
		Property / Symbols used: Q12003 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q12003 / qualifier
			xml-id: C22.S1.XMD1.m1gdec
		Property / Symbols used
			Q11984
		Property / Symbols used: Q11984 / rank
			Normal rank
		Property / Symbols used: Q11984 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11984 / qualifier
			xml-id: C22.S1.XMD4.m1edec
		Property / Symbols used
			Q11988
		Property / Symbols used: Q11988 / rank
			Normal rank
		Property / Symbols used: Q11988 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k^{\prime}}}$ k^{\prime}
		Property / Symbols used: Q11988 / qualifier
			xml-id: C22.S1.XMD5.m1dec

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Latest revision as of 15:31, 2 January 2020

No description defined

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 id

DLMF:22.16.E8

0 references

Symbols used

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2abdec

0 references

Gudermannian function

Defining formula

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

xml-id

C4.S23.E39.m2aadec

0 references

Jacobi’s amplitude function

Defining formula

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

xml-id

C22.S16.E1.m2agdec

0 references

hyperbolic cosine function

Defining formula

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

xml-id

C4.S28.E2.m2adec

0 references

hyperbolic secant function

Defining formula

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

xml-id

C4.S28.E6.m2adec

0 references

hyperbolic sine function

Defining formula

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

xml-id

C4.S28.E1.m2adec

0 references

Q12003

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C22.S1.XMD1.m1gdec

0 references

Q11984

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C22.S1.XMD4.m1edec

0 references

Q11988

Defining formula

${\displaystyle{\displaystyle k^{\prime}}}$

xml-id

C22.S1.XMD5.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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