DLMF:14.5.E18 (Q4730)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:14.5.E18
No description defined

    Statements

    Defining formula
    𝖯 ν - ν ⁡ ( cos ⁡ θ ) = ( sin ⁡ θ ) ν 2 ν ⁢ Γ ⁡ ( ν + 1 ) , Ferrers-Legendre-P-first-kind 𝜈 𝜈 𝜃 superscript 𝜃 𝜈 superscript 2 𝜈 Euler-Gamma 𝜈 1 {\displaystyle{\displaystyle\mathsf{P}^{-\nu}_{\nu}\left(\cos\theta\right)=% \frac{(\sin\theta)^{\nu}}{2^{\nu}\Gamma\left(\nu+1\right)},}}
    0 references
    DLMF id
    DLMF:14.5.E18
    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.m2aedec
    0 references
    Ferrers function of the first kind
    Defining formula
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2addec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aedec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aedec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1kdec
    0 references
    Q11598
    Defining formula
    0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}}
    xml-id
    C14.S5.XMD2.m1ddec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4730&oldid=31099"