DLMF:22.8.E8 (Q6973): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(4 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:

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.m3aadec
Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
test:

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.m2aadec
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.m1gdec
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.m1gdec
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.m1gdec

Latest revision as of 14:03, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:22.8.E8
No description defined

    Statements

    test
    nc ⁡ ( u + v ) = nc ⁡ u ⁢ nc ⁡ v + sc ⁡ u ⁢ dc ⁡ u ⁢ sc ⁡ v ⁢ dc ⁡ v 1 - k ′ 2 ⁢ sc 2 ⁡ u ⁢ sc 2 ⁡ v , Jacobi-elliptic-nc 𝑢 𝑣 𝑘 Jacobi-elliptic-nc 𝑢 𝑘 Jacobi-elliptic-nc 𝑣 𝑘 Jacobi-elliptic-sc 𝑢 𝑘 Jacobi-elliptic-dc 𝑢 𝑘 Jacobi-elliptic-sc 𝑣 𝑘 Jacobi-elliptic-dc 𝑣 𝑘 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 2 𝑢 𝑘 Jacobi-elliptic-sc 2 𝑣 𝑘 {\displaystyle{\displaystyle\operatorname{nc}(u+v)=\frac{\operatorname{nc}u% \operatorname{nc}v+\operatorname{sc}u\operatorname{dc}u\operatorname{sc}v% \operatorname{dc}v}{1-{k^{\prime}}^{2}{\operatorname{sc}^{2}}u{\operatorname{% sc}^{2}}v},}}
    0 references
    DLMF id
    DLMF:22.8.E8
    0 references
    Symbols used
    Jacobian elliptic function
    test
    dc ⁡ ( z , k ) Jacobi-elliptic-dc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m3aadec
    0 references
    Jacobian elliptic function
    test
    nc ⁡ ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m3aadec
    0 references
    Jacobian elliptic function
    test
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m2aadec
    0 references
    Q11991
    test
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C22.S8.XMD1.m1gdec
    0 references
    Q11992
    test
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C22.S8.XMD2.m1gdec
    0 references
    Q11993
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S8.XMD3.m1gdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q6973&oldid=38883"