DLMF:14.5.E3 (Q4715)

From DRMF
Revision as of 01:21, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:14.5.E3
No description defined

    Statements

    Defining formula
    𝖰 ν μ ⁡ ( 0 ) = - 2 μ - 1 ⁢ π 1 / 2 ⁢ sin ⁡ ( 1 2 ⁢ ( ν + μ ) ⁢ π ) ⁢ Γ ⁡ ( 1 2 ⁢ ν + 1 2 ⁢ μ + 1 2 ) Γ ⁡ ( 1 2 ⁢ ν - 1 2 ⁢ μ + 1 ) , Ferrers-Legendre-Q-first-kind 𝜇 𝜈 0 superscript 2 𝜇 1 superscript 𝜋 1 2 1 2 𝜈 𝜇 𝜋 Euler-Gamma 1 2 𝜈 1 2 𝜇 1 2 Euler-Gamma 1 2 𝜈 1 2 𝜇 1 {\displaystyle{\displaystyle\mathsf{Q}^{\mu}_{\nu}\left(0\right)=-\frac{2^{\mu% -1}\pi^{1/2}\sin\left(\frac{1}{2}(\nu+\mu)\pi\right)\Gamma\left(\frac{1}{2}\nu% +\frac{1}{2}\mu+\frac{1}{2}\right)}{\Gamma\left(\frac{1}{2}\nu-\frac{1}{2}\mu+% 1\right)},}}
    0 references
    DLMF id
    DLMF:14.5.E3
    0 references
    constraint
    ν + μ ≠ - 1 , - 3 , - 5 , … 𝜈 𝜇 1 3 5 … {\displaystyle{\displaystyle\nu+\mu\neq-1,-3,-5,\dots}}
    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.m2abdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4715&oldid=30693"