DLMF:14.8.E9 (Q4783): Difference between revisions

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Property / constraint
 

ν - 1 , - 2 , - 3 , 𝜈 1 2 3 {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}

\nu\neq-1,-2,-3,\dots
Property / constraint: ν - 1 , - 2 , - 3 , 𝜈 1 2 3 {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}} / rank
 
Normal rank

Revision as of 16:51, 30 December 2019

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DLMF:14.8.E9
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    Statements

    𝑸 ν ( x ) = - ln ( x - 1 ) 2 Γ ( ν + 1 ) + 1 2 ln 2 - γ - ψ ( ν + 1 ) Γ ( ν + 1 ) + O ( x - 1 ) , shorthand-associated-Legendre-black-Q 𝜈 𝑥 𝑥 1 2 Euler-Gamma 𝜈 1 1 2 2 digamma 𝜈 1 Euler-Gamma 𝜈 1 Big-O 𝑥 1 {\displaystyle{\displaystyle\boldsymbol{Q}_{\nu}\left(x\right)=-\frac{\ln\left% (x-1\right)}{2\Gamma\left(\nu+1\right)}+\frac{\frac{1}{2}\ln 2-\gamma-\psi% \left(\nu+1\right)}{\Gamma\left(\nu+1\right)}+O\left(x-1\right),}}
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    ν - 1 , - 2 , - 3 , 𝜈 1 2 3 {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}
    0 references