DLMF:22.17.E6 (Q7161): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellsnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E4.m2aadec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11985 / rank
 
Normal rank
Property / Symbols used: Q11985 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11985 / qualifier
 
xml-id: C22.S1.XMD3.m1ddec
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.m1edec
Property / Symbols used
 
Property / Symbols used: Q12020 / rank
 
Normal rank
Property / Symbols used: Q12020 / qualifier
 
Defining formula:

k 1 subscript 𝑘 1 {\displaystyle{\displaystyle k_{1}}}

k_{1}
Property / Symbols used: Q12020 / qualifier
 
xml-id: C22.S17.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12021 / rank
 
Normal rank
Property / Symbols used: Q12021 / qualifier
 
Defining formula:

k 1 superscript subscript 𝑘 1 {\displaystyle{\displaystyle k_{1}^{\prime}}}

k_{1}^{\prime}
Property / Symbols used: Q12021 / qualifier
 
xml-id: C22.S17.XMD2.m1adec

Latest revision as of 15:38, 2 January 2020

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DLMF:22.17.E6
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    Statements

    sn ( z , i k ) = k 1 sd ( z / k 1 , k 1 ) , Jacobi-elliptic-sn 𝑧 𝑖 𝑘 superscript subscript 𝑘 1 Jacobi-elliptic-sd 𝑧 superscript subscript 𝑘 1 subscript 𝑘 1 {\displaystyle{\displaystyle\operatorname{sn}\left(z,ik\right)=k_{1}^{\prime}% \operatorname{sd}\left(z/k_{1}^{\prime},k_{1}\right),}}
    0 references
    DLMF:22.17.E6
    0 references
    sd ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E7.m2adec
    0 references
    sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m2aadec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C22.S1.XMD3.m1ddec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1edec
    0 references
    k 1 subscript 𝑘 1 {\displaystyle{\displaystyle k_{1}}}
    C22.S17.XMD1.m1adec
    0 references
    k 1 superscript subscript 𝑘 1 {\displaystyle{\displaystyle k_{1}^{\prime}}}
    C22.S17.XMD2.m1adec
    0 references