DLMF:14.5.E17 (Q4729): 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.m2ajdec

Revision as of 00:23, 2 January 2020

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DLMF:14.5.E17
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    Statements

    test
    𝑸 ν ± 1 / 2 ⁡ ( cosh ⁡ ξ ) = ( π 2 ⁢ sinh ⁡ ξ ) 1 / 2 ⁢ exp ⁡ ( - ( ν + 1 2 ) ⁢ ξ ) Γ ⁡ ( ν + 3 2 ) . associated-Legendre-black-Q plus-or-minus 1 2 𝜈 𝜉 superscript 𝜋 2 𝜉 1 2 𝜈 1 2 𝜉 Euler-Gamma 𝜈 3 2 {\displaystyle{\displaystyle\boldsymbol{Q}^{\pm 1/2}_{\nu}\left(\cosh\xi\right% )=\left(\frac{\pi}{2\sinh\xi}\right)^{1/2}\frac{\exp\left(-\left(\nu+\frac{1}{% 2}\right)\xi\right)}{\Gamma\left(\nu+\frac{3}{2}\right)}.}}
    0 references
    DLMF id
    DLMF:14.5.E17
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
    0 references
    Q11592
    test
    𝑸 ν μ ⁡ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m3adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
     
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