DLMF:22.8.E7 (Q6972): 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
 
Defining formula:

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

\Jacobiellnck@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E5.m3adec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

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

\Jacobiellsck@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E9.m2adec
Property / Symbols used
 
Property / Symbols used: Q11991 / rank
 
Normal rank
Property / Symbols used: Q11991 / qualifier
 
Defining formula:

u 𝑢 {\displaystyle{\displaystyle u}}

u
Property / Symbols used: Q11991 / qualifier
 
xml-id: C22.S8.XMD1.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11992 / rank
 
Normal rank
Property / Symbols used: Q11992 / qualifier
 
Defining formula:

v 𝑣 {\displaystyle{\displaystyle v}}

v
Property / Symbols used: Q11992 / qualifier
 
xml-id: C22.S8.XMD2.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11993 / rank
 
Normal rank
Property / Symbols used: Q11993 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11993 / qualifier
 
xml-id: C22.S8.XMD3.m1fdec

Latest revision as of 15:02, 2 January 2020

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English
DLMF:22.8.E7
No description defined

    Statements

    Defining formula
    dc ⁡ ( u + v ) = dc ⁡ u ⁢ dc ⁡ v + k ′ 2 ⁢ sc ⁡ u ⁢ nc ⁡ u ⁢ sc ⁡ v ⁢ nc ⁡ v 1 - k ′ 2 ⁢ sc 2 ⁡ u ⁢ sc 2 ⁡ v , Jacobi-elliptic-dc 𝑢 𝑣 𝑘 Jacobi-elliptic-dc 𝑢 𝑘 Jacobi-elliptic-dc 𝑣 𝑘 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 𝑢 𝑘 Jacobi-elliptic-nc 𝑢 𝑘 Jacobi-elliptic-sc 𝑣 𝑘 Jacobi-elliptic-nc 𝑣 𝑘 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 2 𝑢 𝑘 Jacobi-elliptic-sc 2 𝑣 𝑘 {\displaystyle{\displaystyle\operatorname{dc}(u+v)=\frac{\operatorname{dc}u% \operatorname{dc}v+{k^{\prime}}^{2}\operatorname{sc}u\operatorname{nc}u% \operatorname{sc}v\operatorname{nc}v}{1-{k^{\prime}}^{2}{\operatorname{sc}^{2}% }u{\operatorname{sc}^{2}}v},}}
    0 references
    DLMF id
    DLMF:22.8.E7
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    dc ⁡ ( z , k ) Jacobi-elliptic-dc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m3adec
    0 references
    Jacobian elliptic function
    Defining formula
    nc ⁡ ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m3adec
    0 references
    Jacobian elliptic function
    Defining formula
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m2adec
    0 references
    Q11991
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C22.S8.XMD1.m1fdec
    0 references
    Q11992
    Defining formula
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C22.S8.XMD2.m1fdec
    0 references
    Q11993
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S8.XMD3.m1fdec
    0 references
     
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