DLMF:22.7.E6 (Q6963): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(5 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

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

\Jacobielldnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E6.m2abdec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11985 / rank
 
Normal rank
Property / Symbols used: Q11985 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11985 / qualifier
 
xml-id: C22.S1.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11989 / rank
 
Normal rank
Property / Symbols used: Q11989 / qualifier
 
test:

k 2 subscript 𝑘 2 {\displaystyle{\displaystyle k_{2}}}

k_{2}
Property / Symbols used: Q11989 / qualifier
 
xml-id: C22.S7.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11990 / rank
 
Normal rank
Property / Symbols used: Q11990 / qualifier
 
test:

k 2 ′ superscript subscript 𝑘 2 ′ {\displaystyle{\displaystyle k_{2}^{\prime}}}

k_{2}^{\prime}
Property / Symbols used: Q11990 / qualifier
 
xml-id: C22.S7.XMD3.m1adec

Latest revision as of 14:01, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:22.7.E6
No description defined

    Statements

    test
    sn ⁡ ( z , k ) = ( 1 + k 2 ′ ) ⁢ sn ⁡ ( z / ( 1 + k 2 ′ ) , k 2 ) ⁢ cn ⁡ ( z / ( 1 + k 2 ′ ) , k 2 ) dn ⁡ ( z / ( 1 + k 2 ′ ) , k 2 ) , Jacobi-elliptic-sn 𝑧 𝑘 1 superscript subscript 𝑘 2 ′ Jacobi-elliptic-sn 𝑧 1 superscript subscript 𝑘 2 ′ subscript 𝑘 2 Jacobi-elliptic-cn 𝑧 1 superscript subscript 𝑘 2 ′ subscript 𝑘 2 Jacobi-elliptic-dn 𝑧 1 superscript subscript 𝑘 2 ′ subscript 𝑘 2 {\displaystyle{\displaystyle\operatorname{sn}\left(z,k\right)=\frac{(1+k_{2}^{% \prime})\operatorname{sn}\left(z/(1+k_{2}^{\prime}),k_{2}\right)\operatorname{% cn}\left(z/(1+k_{2}^{\prime}),k_{2}\right)}{\operatorname{dn}\left(z/(1+k_{2}^% {\prime}),k_{2}\right)},}}
    0 references
    DLMF id
    DLMF:22.7.E6
    0 references
    Symbols used
    Jacobian elliptic function
    test
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2aadec
    0 references
    Jacobian elliptic function
    test
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2abdec
    0 references
    Jacobian elliptic function
    test
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2abdec
    0 references
    Q11985
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1cdec
    0 references
    Q11984
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1ddec
    0 references
    Q11989
    test
    k 2 subscript 𝑘 2 {\displaystyle{\displaystyle k_{2}}}
    xml-id
    C22.S7.XMD2.m1adec
    0 references
    Q11990
    test
    k 2 ′ superscript subscript 𝑘 2 ′ {\displaystyle{\displaystyle k_{2}^{\prime}}}
    xml-id
    C22.S7.XMD3.m1adec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q6963&oldid=38814"