DLMF:22.14.E17 (Q7092): Difference between revisions

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Revision as of 15:26, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:26, 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
			principal branch of logarithm function
		Property / Symbols used: principal branch of logarithm function / rank
			Normal rank
		Property / Symbols used: principal branch of logarithm function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ln\NVar{z}}}$ \ln@@{\NVar{z}}
		Property / Symbols used: principal branch of logarithm function / qualifier
			xml-id: C4.S2.E2.m2akdec
		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.m1pdec
		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.m1ddec

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Latest revision as of 15:26, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:22.14.E17	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{K\left(k\right)}\ln\left(\operatorname{cn}\left(t,k\right)\right)\mathrm{d}t=-\tfrac{1}{4}{K^{\prime}}\left(k\right)+\tfrac{1}{2}K\left(k\right)\ln\left(k^{\prime}/k\right),}}$

0 references

DLMF id

DLMF:22.14.E17

0 references

Symbols used

Jacobian elliptic function

Defining formula

${\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}$

xml-id

C22.S2.E5.m2aedec

0 references

Q11821

Defining formula

${\displaystyle{\displaystyle{K^{\prime}}\left(\NVar{k}\right)}}$

xml-id

C19.S2.E9.m1aadec

0 references

Q11600

Defining formula

${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$

xml-id

C19.S2.E8.m1aadec

0 references

Q10770

Defining formula

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

xml-id

C1.S4.SS4.m1apdec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3apdec

0 references

principal branch of logarithm function

Defining formula

${\displaystyle{\displaystyle\ln\NVar{z}}}$

xml-id

C4.S2.E2.m2akdec

0 references

Q11984

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C22.S1.XMD4.m1pdec

0 references

Q11988

Defining formula

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

xml-id

C22.S1.XMD5.m1ddec

0 references

 

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