DLMF:14.19.E5 (Q4918): Difference between revisions

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Property / constraint
 

m < n + 1 2 𝑚 𝑛 1 2 {\displaystyle{\displaystyle m<n+\tfrac{1}{2}}}

m<n+\tfrac{1}{2}
Property / constraint: m < n + 1 2 𝑚 𝑛 1 2 {\displaystyle{\displaystyle m<n+\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 17:53, 30 December 2019

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DLMF:14.19.E5
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    Statements

    Defining formula
    𝑸 n - 1 2 m ⁡ ( cosh ⁡ ξ ) = Γ ⁡ ( n + 1 2 ) Γ ⁡ ( n + m + 1 2 ) ⁢ Γ ⁡ ( n - m + 1 2 ) ⁢ ∫ 0 ∞ cosh ⁡ ( m ⁢ t ) ( cosh ⁡ ξ + cosh ⁡ t ⁢ sinh ⁡ ξ ) n + ( 1 / 2 ) ⁢ d t , associated-Legendre-black-Q 𝑚 𝑛 1 2 𝜉 Euler-Gamma 𝑛 1 2 Euler-Gamma 𝑛 𝑚 1 2 Euler-Gamma 𝑛 𝑚 1 2 superscript subscript 0 𝑚 𝑡 superscript 𝜉 𝑡 𝜉 𝑛 1 2 𝑡 {\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n-\frac{1}{2}}\left(\cosh\xi% \right)=\frac{\Gamma\left(n+\frac{1}{2}\right)}{\Gamma\left(n+m+\tfrac{1}{2}% \right)\Gamma\left(n-m+\frac{1}{2}\right)}\*\int_{0}^{\infty}\frac{\cosh\left(% mt\right)}{(\cosh\xi+\cosh t\sinh\xi)^{n+(1/2)}}\mathrm{d}t,}}
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    DLMF id
    DLMF:14.19.E5
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    constraint
    m < n + 1 2 𝑚 𝑛 1 2 {\displaystyle{\displaystyle m<n+\tfrac{1}{2}}}
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