DLMF:14.5.E15 (Q4727)

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DLMF:14.5.E15
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    Statements

    Defining formula
    P ν 1 / 2 ⁡ ( cosh ⁡ ξ ) = ( 2 π ⁢ sinh ⁡ ξ ) 1 / 2 ⁢ cosh ⁡ ( ( ν + 1 2 ) ⁢ ξ ) , Legendre-P-first-kind 1 2 𝜈 𝜉 superscript 2 𝜋 𝜉 1 2 𝜈 1 2 𝜉 {\displaystyle{\displaystyle P^{1/2}_{\nu}\left(\cosh\xi\right)=\left(\frac{2}% {\pi\sinh\xi}\right)^{1/2}\cosh\left(\left(\nu+\tfrac{1}{2}\right)\xi\right),}}
    0 references
    DLMF id
    DLMF:14.5.E15
    0 references
    Symbols used
    Q11481
    Defining formula
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1adec
    0 references
     
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