DLMF:22.8.E16 (Q6981): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11995 / rank
 
Normal rank
Property / Symbols used: Q11995 / qualifier
 
Defining formula:

v 𝑣 {\displaystyle{\displaystyle v}}

v
Property / Symbols used: Q11995 / qualifier
 
xml-id: C22.S8.XMD5.m1cdec

Revision as of 15:04, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:22.8.E16
No description defined

    Statements

    Defining formula
    cn ⁡ ( u + v ) = 1 - sn 2 ⁡ u - sn 2 ⁡ v + k 2 ⁢ sn 2 ⁡ u ⁢ sn 2 ⁡ v cn ⁡ u ⁢ cn ⁡ v + sn ⁡ u ⁢ dn ⁡ u ⁢ sn ⁡ v ⁢ dn ⁡ v , Jacobi-elliptic-cn 𝑢 𝑣 𝑘 1 Jacobi-elliptic-sn 2 𝑢 𝑘 Jacobi-elliptic-sn 2 𝑣 𝑘 superscript 𝑘 2 Jacobi-elliptic-sn 2 𝑢 𝑘 Jacobi-elliptic-sn 2 𝑣 𝑘 Jacobi-elliptic-cn 𝑢 𝑘 Jacobi-elliptic-cn 𝑣 𝑘 Jacobi-elliptic-sn 𝑢 𝑘 Jacobi-elliptic-dn 𝑢 𝑘 Jacobi-elliptic-sn 𝑣 𝑘 Jacobi-elliptic-dn 𝑣 𝑘 {\displaystyle{\displaystyle\operatorname{cn}(u+v)=\frac{1-{\operatorname{sn}^% {2}}u-{\operatorname{sn}^{2}}v+k^{2}{\operatorname{sn}^{2}}u{\operatorname{sn}% ^{2}}v}{\operatorname{cn}u\operatorname{cn}v+\operatorname{sn}u\operatorname{% dn}u\operatorname{sn}v\operatorname{dn}v},}}
    0 references
    DLMF id
    DLMF:22.8.E16
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2afdec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2afdec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2afdec
    0 references
    Q11994
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C22.S8.XMD4.m1cdec
    0 references
    Q11995
    Defining formula
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C22.S8.XMD5.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6981&oldid=53980"