DLMF:22.11.E10 (Q7034): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: secant function / rank
 
Normal rank
Property / Symbols used: secant function / qualifier
 
Defining formula:

sec ⁡ z 𝑧 {\displaystyle{\displaystyle\sec\NVar{z}}}

\sec@@{\NVar{z}}
Property / Symbols used: secant function / qualifier
 
xml-id: C4.S14.E6.m2adec

Revision as of 15:14, 2 January 2020

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DLMF:22.11.E10
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    Statements

    Defining formula
    dc ⁡ ( z , k ) - π 2 ⁢ K ⁢ sec ⁡ ζ = 2 ⁢ π K ⁢ ∑ n = 0 ∞ ( - 1 ) n ⁢ q 2 ⁢ n + 1 ⁢ cos ⁡ ( ( 2 ⁢ n + 1 ) ⁢ ζ ) 1 - q 2 ⁢ n + 1 , Jacobi-elliptic-dc 𝑧 𝑘 𝜋 2 𝐾 𝜁 2 𝜋 𝐾 superscript subscript 𝑛 0 superscript 1 𝑛 superscript 𝑞 2 𝑛 1 2 𝑛 1 𝜁 1 superscript 𝑞 2 𝑛 1 {\displaystyle{\displaystyle\operatorname{dc}\left(z,k\right)-\frac{\pi}{2K}% \sec\zeta=\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos\left((2n% +1)\zeta\right)}{1-q^{2n+1}},}}
    0 references
    DLMF id
    DLMF:22.11.E10
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    dc ⁡ ( z , k ) Jacobi-elliptic-dc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m3adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    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.m1aidec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
    0 references
    nome
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C22.S2.E1.m2aidec
    0 references
    secant function
    Defining formula
    sec ⁡ z 𝑧 {\displaystyle{\displaystyle\sec\NVar{z}}}
    xml-id
    C4.S14.E6.m2adec
    0 references
     
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