DLMF:14.19.E8 (Q4921): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11481 / rank
 
Normal rank
Property / Symbols used: Q11481 / qualifier
 
Defining formula:

P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\assLegendreP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11481 / qualifier
 
xml-id: C14.S21.SS1.p1.m1acdec

Revision as of 13:31, 2 January 2020

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DLMF:14.19.E8
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    Statements

    Defining formula
    𝑸 n - 1 2 m ⁡ ( cosh ⁡ ξ ) = Γ ⁡ ( m - n + 1 2 ) Γ ⁡ ( m + n + 1 2 ) ⁢ ( π 2 ⁢ sinh ⁡ ξ ) 1 / 2 ⁢ P m - 1 2 n ⁡ ( coth ⁡ ξ ) . associated-Legendre-black-Q 𝑚 𝑛 1 2 𝜉 Euler-Gamma 𝑚 𝑛 1 2 Euler-Gamma 𝑚 𝑛 1 2 superscript 𝜋 2 𝜉 1 2 Legendre-P-first-kind 𝑛 𝑚 1 2 hyperbolic-cotangent 𝜉 {\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n-\frac{1}{2}}\left(\cosh\xi% \right)=\frac{\Gamma\left(m-n+\tfrac{1}{2}\right)}{\Gamma\left(m+n+\tfrac{1}{2% }\right)}\*\left(\frac{\pi}{2\sinh\xi}\right)^{1/2}P^{n}_{m-\frac{1}{2}}\left(% \coth\xi\right).}}
    0 references
    DLMF id
    DLMF:14.19.E8
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aedec
    0 references
    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.m1acdec
    0 references
     
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