DLMF:14.12.E1 (Q4822): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / constraint
 

ℜ ⁡ μ < 1 2 𝜇 1 2 {\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}}

\Re\mu<\tfrac{1}{2}
Property / constraint: ℜ ⁡ μ < 1 2 𝜇 1 2 {\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 17:52, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:14.12.E1
No description defined

    Statements

    Defining formula
    𝖯 ν μ ⁡ ( cos ⁡ θ ) = 2 1 / 2 ⁢ ( sin ⁡ θ ) μ π 1 / 2 ⁢ Γ ⁡ ( 1 2 - μ ) ⁢ ∫ 0 θ cos ⁡ ( ( ν + 1 2 ) ⁢ t ) ( cos ⁡ t - cos ⁡ θ ) μ + ( 1 / 2 ) ⁢ d t , Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝜃 superscript 2 1 2 superscript 𝜃 𝜇 superscript 𝜋 1 2 Euler-Gamma 1 2 𝜇 superscript subscript 0 𝜃 𝜈 1 2 𝑡 superscript 𝑡 𝜃 𝜇 1 2 𝑡 {\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(\cos\theta\right)=% \frac{2^{1/2}(\sin\theta)^{\mu}}{\pi^{1/2}\Gamma\left(\frac{1}{2}-\mu\right)}% \int_{0}^{\theta}\frac{\cos\left(\left(\nu+\frac{1}{2}\right)t\right)}{(\cos t% -\cos\theta)^{\mu+(1/2)}}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:14.12.E1
    0 references
    constraint
    ℜ ⁡ μ < 1 2 𝜇 1 2 {\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}}
    0 references
    0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}}
    0 references
    ℜ ⁡ μ < 1 2 𝜇 1 2 {\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}}
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4822&oldid=18901"