DLMF:22.14.E12 (Q7087): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3akdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

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

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2agdec
Property / Symbols used
 
Property / Symbols used: Q12003 / rank
 
Normal rank
Property / Symbols used: Q12003 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12003 / qualifier
 
xml-id: C22.S1.XMD1.m1kdec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1kdec

Latest revision as of 15:25, 2 January 2020

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DLMF:22.14.E12
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    Statements

    cs ( x , k ) d x = ln ( ns ( x , k ) - ds ( x , k ) ) . Jacobi-elliptic-cs 𝑥 𝑘 𝑥 Jacobi-elliptic-ns 𝑥 𝑘 Jacobi-elliptic-ds 𝑥 𝑘 {\displaystyle{\displaystyle\int\operatorname{cs}\left(x,k\right)\mathrm{d}x=% \ln\left(\operatorname{ns}\left(x,k\right)-\operatorname{ds}\left(x,k\right)% \right).}}
    0 references
    DLMF:22.14.E12
    0 references
    cs ( z , k ) Jacobi-elliptic-cs 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cs}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E9.m3abdec
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    ds ( z , k ) Jacobi-elliptic-ds 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E7.m3abdec
    0 references
    ns ( z , k ) Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m3abdec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1akdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3akdec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2agdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C22.S1.XMD1.m1kdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1kdec
    0 references