DLMF:22.8.E4 (Q6969): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

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

\Jacobiellcdk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E8.m2adec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

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

\Jacobiellndk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E6.m3adec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

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

\Jacobiellsdk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E7.m2adec
Property / Symbols used
 
Property / Symbols used: Q11991 / rank
 
Normal rank
Property / Symbols used: Q11991 / qualifier
 
test:

u 𝑢 {\displaystyle{\displaystyle u}}

u
Property / Symbols used: Q11991 / qualifier
 
xml-id: C22.S8.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11992 / rank
 
Normal rank
Property / Symbols used: Q11992 / qualifier
 
test:

v 𝑣 {\displaystyle{\displaystyle v}}

v
Property / Symbols used: Q11992 / qualifier
 
xml-id: C22.S8.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11993 / rank
 
Normal rank
Property / Symbols used: Q11993 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11993 / qualifier
 
xml-id: C22.S8.XMD3.m1cdec

Latest revision as of 14:02, 2 January 2020

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DLMF:22.8.E4
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    Statements

    test
    cd ⁡ ( u + v ) = cd ⁡ u ⁢ cd ⁡ v - k ′ 2 ⁢ sd ⁡ u ⁢ nd ⁡ u ⁢ sd ⁡ v ⁢ nd ⁡ v 1 + k 2 ⁢ k ′ 2 ⁢ sd 2 ⁡ u ⁢ sd 2 ⁡ v , Jacobi-elliptic-cd 𝑢 𝑣 𝑘 Jacobi-elliptic-cd 𝑢 𝑘 Jacobi-elliptic-cd 𝑣 𝑘 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sd 𝑢 𝑘 Jacobi-elliptic-nd 𝑢 𝑘 Jacobi-elliptic-sd 𝑣 𝑘 Jacobi-elliptic-nd 𝑣 𝑘 1 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sd 2 𝑢 𝑘 Jacobi-elliptic-sd 2 𝑣 𝑘 {\displaystyle{\displaystyle\operatorname{cd}(u+v)=\frac{\operatorname{cd}u% \operatorname{cd}v-{k^{\prime}}^{2}\operatorname{sd}u\operatorname{nd}u% \operatorname{sd}v\operatorname{nd}v}{1+k^{2}{k^{\prime}}^{2}{\operatorname{sd% }^{2}}u{\operatorname{sd}^{2}}v},}}
    0 references
    DLMF id
    DLMF:22.8.E4
    0 references
    Symbols used
    Jacobian elliptic function
    test
    cd ⁡ ( z , k ) Jacobi-elliptic-cd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m2adec
    0 references
    Jacobian elliptic function
    test
    nd ⁡ ( z , k ) Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m3adec
    0 references
    Jacobian elliptic function
    test
    sd ⁡ ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m2adec
    0 references
    Q11991
    test
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C22.S8.XMD1.m1cdec
    0 references
    Q11992
    test
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C22.S8.XMD2.m1cdec
    0 references
    Q11993
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S8.XMD3.m1cdec
    0 references
     
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