DLMF:14.5.E26 (Q4738): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11600 / rank
 
Normal rank
Property / Symbols used: Q11600 / qualifier
 
test:

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.m1aedec

Revision as of 00:25, 2 January 2020

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Language Label Description Also known as
English
DLMF:14.5.E26
No description defined

    Statements

    test
    𝑸 1 2 ⁡ ( cosh ⁡ ξ ) = 2 ⁢ π - 1 / 2 ⁢ cosh ⁡ ξ ⁢ sech ⁡ ( 1 2 ⁢ ξ ) ⁢ K ⁡ ( sech ⁡ ( 1 2 ⁢ ξ ) ) - 4 ⁢ π - 1 / 2 ⁢ cosh ⁡ ( 1 2 ⁢ ξ ) ⁢ E ⁡ ( sech ⁡ ( 1 2 ⁢ ξ ) ) , shorthand-associated-Legendre-black-Q 1 2 𝜉 2 superscript 𝜋 1 2 𝜉 1 2 𝜉 complete-elliptic-integral-first-kind-K 1 2 𝜉 4 superscript 𝜋 1 2 1 2 𝜉 complete-elliptic-integral-second-kind-E 1 2 𝜉 {\displaystyle{\displaystyle\boldsymbol{Q}_{\frac{1}{2}}\left(\cosh\xi\right)=% 2\pi^{-1/2}\cosh\xi\operatorname{sech}\left(\tfrac{1}{2}\xi\right)K\left(% \operatorname{sech}\left(\tfrac{1}{2}\xi\right)\right)-4\pi^{-1/2}\cosh\left(% \tfrac{1}{2}\xi\right)E\left(\operatorname{sech}\left(\tfrac{1}{2}\xi\right)% \right),}}
    0 references
    DLMF id
    DLMF:14.5.E26
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aodec
    0 references
    Q11600
    test
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1aedec
    0 references
     
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