DLMF:22.8.E10 (Q6975): 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:

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

\Jacobiellcsk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E9.m3adec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

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

\Jacobielldsk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E7.m3adec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

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

\Jacobiellnsk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E4.m3adec
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.m1idec
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.m1idec
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.m1idec

Latest revision as of 15:03, 2 January 2020

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DLMF:22.8.E10
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    Statements

    Defining formula
    ns ⁡ ( u + v ) = ns ⁡ u ⁢ ds ⁡ v ⁢ cs ⁡ v - ns ⁡ v ⁢ ds ⁡ u ⁢ cs ⁡ u cs 2 ⁡ v - cs 2 ⁡ u , Jacobi-elliptic-ns 𝑢 𝑣 𝑘 Jacobi-elliptic-ns 𝑢 𝑘 Jacobi-elliptic-ds 𝑣 𝑘 Jacobi-elliptic-cs 𝑣 𝑘 Jacobi-elliptic-ns 𝑣 𝑘 Jacobi-elliptic-ds 𝑢 𝑘 Jacobi-elliptic-cs 𝑢 𝑘 Jacobi-elliptic-cs 2 𝑣 𝑘 Jacobi-elliptic-cs 2 𝑢 𝑘 {\displaystyle{\displaystyle\operatorname{ns}(u+v)=\frac{\operatorname{ns}u% \operatorname{ds}v\operatorname{cs}v-\operatorname{ns}v\operatorname{ds}u% \operatorname{cs}u}{{\operatorname{cs}^{2}}v-{\operatorname{cs}^{2}}u},}}
    0 references
    DLMF id
    DLMF:22.8.E10
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cs ⁡ ( z , k ) Jacobi-elliptic-cs 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cs}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m3adec
    0 references
    Jacobian elliptic function
    Defining formula
    ds ⁡ ( z , k ) Jacobi-elliptic-ds 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m3adec
    0 references
    Jacobian elliptic function
    Defining formula
    ns ⁡ ( z , k ) Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m3adec
    0 references
    Q11991
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C22.S8.XMD1.m1idec
    0 references
    Q11992
    Defining formula
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C22.S8.XMD2.m1idec
    0 references
    Q11993
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S8.XMD3.m1idec
    0 references
     
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