DLMF:22.11.E2 (Q7026): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2adec
Property / Symbols used
 
Property / Symbols used: nome / rank
 
Normal rank
Property / Symbols used: nome / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: nome / qualifier
 
xml-id: C22.S2.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11985 / rank
 
Normal rank
Property / Symbols used: Q11985 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11985 / qualifier
 
xml-id: C22.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11986 / rank
 
Normal rank
Property / Symbols used: Q11986 / qualifier
 
Defining formula:

ζ 𝜁 {\displaystyle{\displaystyle\zeta}}

\zeta
Property / Symbols used: Q11986 / qualifier
 
xml-id: C22.S2.XMD2.m1adec

Latest revision as of 15:11, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:22.11.E2
No description defined

    Statements

    cn ( z , k ) = 2 π K k n = 0 q n + 1 2 cos ( ( 2 n + 1 ) ζ ) 1 + q 2 n + 1 , Jacobi-elliptic-cn 𝑧 𝑘 2 𝜋 𝐾 𝑘 superscript subscript 𝑛 0 superscript 𝑞 𝑛 1 2 2 𝑛 1 𝜁 1 superscript 𝑞 2 𝑛 1 {\displaystyle{\displaystyle\operatorname{cn}\left(z,k\right)=\frac{2\pi}{Kk}% \sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\cos\left((2n+1)\zeta\right)}{1+q^{2% n+1}},}}
    0 references
    DLMF:22.11.E2
    0 references
    cn ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E5.m2adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    K ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    C19.S2.E8.m1aadec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
    0 references
    q 𝑞 {\displaystyle{\displaystyle q}}
    C22.S2.E1.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C22.S1.XMD3.m1adec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1adec
    0 references
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    C22.S2.XMD2.m1adec
    0 references