DLMF:14.5.E4 (Q4716): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / constraint
 

ν + μ - 2 , - 4 , - 6 , 𝜈 𝜇 2 4 6 {\displaystyle{\displaystyle\nu+\mu\neq-2,-4,-6,\dots}}

\nu+\mu\neq-2,-4,-6,\dots
Property / constraint: ν + μ - 2 , - 4 , - 6 , 𝜈 𝜇 2 4 6 {\displaystyle{\displaystyle\nu+\mu\neq-2,-4,-6,\dots}} / rank
 
Normal rank

Revision as of 17:51, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:14.5.E4
No description defined

    Statements

    d 𝖰 ν μ ( x ) d x | x = 0 = 2 μ π 1 / 2 cos ( 1 2 ( ν + μ ) π ) Γ ( 1 2 ν + 1 2 μ + 1 ) Γ ( 1 2 ν - 1 2 μ + 1 2 ) , evaluated-at derivative Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 𝑥 𝑥 0 superscript 2 𝜇 superscript 𝜋 1 2 1 2 𝜈 𝜇 𝜋 Euler-Gamma 1 2 𝜈 1 2 𝜇 1 Euler-Gamma 1 2 𝜈 1 2 𝜇 1 2 {\displaystyle{\displaystyle\left.\frac{\mathrm{d}\mathsf{Q}^{\mu}_{\nu}\left(% x\right)}{\mathrm{d}x}\right|_{x=0}=\frac{2^{\mu}\pi^{1/2}\cos\left(\frac{1}{2% }(\nu+\mu)\pi\right)\Gamma\left(\frac{1}{2}\nu+\frac{1}{2}\mu+1\right)}{\Gamma% \left(\frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}\right)},}}
    0 references
    DLMF:14.5.E4
    0 references
    ν + μ - 2 , - 4 , - 6 , 𝜈 𝜇 2 4 6 {\displaystyle{\displaystyle\nu+\mu\neq-2,-4,-6,\dots}}
    0 references