DLMF:22.16.E9 (Q7128): Difference between revisions

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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
 
test:

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.m2aadec

Revision as of 14:32, 2 January 2020

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DLMF:22.16.E9
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    Statements

    test
    am ⁡ ( x , k ) = π 2 ⁢ K ⁢ x + 2 ⁢ ∑ n = 1 ∞ q n ⁢ sin ⁡ ( 2 ⁢ n ⁢ ζ ) n ⁢ ( 1 + q 2 ⁢ n ) . Jacobi-elliptic-amplitude 𝑥 𝑘 𝜋 2 𝐾 𝑥 2 superscript subscript 𝑛 1 superscript 𝑞 𝑛 2 𝑛 𝜁 𝑛 1 superscript 𝑞 2 𝑛 {\displaystyle{\displaystyle\operatorname{am}\left(x,k\right)=\frac{\pi}{2K}x+% 2\sum_{n=1}^{\infty}\frac{q^{n}\sin\left(2n\zeta\right)}{n(1+q^{2n})}.}}
    0 references
    DLMF id
    DLMF:22.16.E9
    0 references
    Symbols used
    Jacobi’s amplitude function
    test
    am ⁡ ( x , k ) Jacobi-elliptic-amplitude 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S16.E1.m2ahdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
     
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