DLMF:22.11.E12 (Q7036): Difference between revisions

From DRMF
Jump to navigation Jump to search
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
(9 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
 
Defining formula:

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.m2adec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2akdec
Property / Symbols used
 
Property / Symbols used: Q11600 / rank
 
Normal rank
Property / Symbols used: Q11600 / qualifier
 
Defining formula:

K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}

\compellintKk@{\NVar{k}}
Property / Symbols used: Q11600 / qualifier
 
xml-id: C19.S2.E8.m1akdec
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.m2akdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aedec
Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
Defining formula:

tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2adec
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.m1kdec
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.m1kdec
Property / Symbols used
 
Property / Symbols used: Q11988 / rank
 
Normal rank
Property / Symbols used: Q11988 / qualifier
 
Defining formula:

k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11988 / qualifier
 
xml-id: C22.S1.XMD5.m1cdec
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.m1kdec

Latest revision as of 15:14, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:22.11.E12
No description defined

    Statements

    Defining formula
    sc ⁡ ( z , k ) - π 2 ⁢ K ⁢ k ′ ⁢ tan ⁡ ζ = 2 ⁢ π K ⁢ k ′ ⁢ ∑ n = 1 ∞ ( - 1 ) n ⁢ q 2 ⁢ n ⁢ sin ⁡ ( 2 ⁢ n ⁢ ζ ) 1 + q 2 ⁢ n . Jacobi-elliptic-sc 𝑧 𝑘 𝜋 2 𝐾 superscript 𝑘 ′ 𝜁 2 𝜋 𝐾 superscript 𝑘 ′ superscript subscript 𝑛 1 superscript 1 𝑛 superscript 𝑞 2 𝑛 2 𝑛 𝜁 1 superscript 𝑞 2 𝑛 {\displaystyle{\displaystyle\operatorname{sc}\left(z,k\right)-\frac{\pi}{2Kk^{% \prime}}\tan\zeta=\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{% 2n}\sin\left(2n\zeta\right)}{1+q^{2n}}.}}
    0 references
    DLMF id
    DLMF:22.11.E12
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1akdec
    0 references
    nome
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C22.S2.E1.m2akdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aedec
    0 references
    tangent function
    Defining formula
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2adec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1kdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1kdec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1cdec
    0 references
    Q11986
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C22.S2.XMD2.m1kdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7036&oldid=55801"