DLMF:19.5.E8 (Q6137): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m1abdec

Revision as of 13:40, 2 January 2020

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DLMF:19.5.E8
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    Statements

    Defining formula
    K ⁡ ( k ) = π 2 ⁢ ( 1 + 2 ⁢ ∑ n = 1 ∞ q n 2 ) 2 , complete-elliptic-integral-first-kind-K 𝑘 𝜋 2 superscript 1 2 superscript subscript 𝑛 1 superscript 𝑞 superscript 𝑛 2 2 {\displaystyle{\displaystyle K\left(k\right)=\frac{\pi}{2}\left(1+2\sum_{n=1}^% {\infty}q^{n^{2}}\right)^{2},}}
    0 references
    DLMF id
    DLMF:19.5.E8
    0 references
    constraint
    | q | < 1 𝑞 1 {\displaystyle{\displaystyle|q|<1}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    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.m1abdec
    0 references
     
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