DLMF:14.5.E2 (Q4714): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1adec

Latest revision as of 01:21, 2 January 2020

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DLMF:14.5.E2
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    Statements

    Defining formula
    d 𝖯 ν μ ⁡ ( x ) d x | x = 0 = - 2 μ + 1 ⁢ π 1 / 2 Γ ⁡ ( 1 2 ⁢ ν - 1 2 ⁢ μ + 1 2 ) ⁢ Γ ⁡ ( - 1 2 ⁢ ν - 1 2 ⁢ μ ) , evaluated-at derivative Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝑥 𝑥 0 superscript 2 𝜇 1 superscript 𝜋 1 2 Euler-Gamma 1 2 𝜈 1 2 𝜇 1 2 Euler-Gamma 1 2 𝜈 1 2 𝜇 {\displaystyle{\displaystyle\left.\frac{\mathrm{d}\mathsf{P}^{\mu}_{\nu}\left(% x\right)}{\mathrm{d}x}\right|_{x=0}=-\frac{2^{\mu+1}\pi^{1/2}}{\Gamma\left(% \frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}\right)\Gamma\left(-\frac{1}{2}\nu-% \frac{1}{2}\mu\right)},}}
    0 references
    DLMF id
    DLMF:14.5.E2
    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.m2aadec
    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.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1dec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1adec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1adec
    0 references
     
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