DLMF:18.17.E9 (Q5750): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1fdec

Latest revision as of 15:46, 2 January 2020

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DLMF:18.17.E9
No description defined

    Statements

    Defining formula
    ( 1 - x ) α + μ ⁢ P n ( α + μ , β - μ ) ⁡ ( x ) Γ ⁡ ( α + μ + n + 1 ) = ∫ x 1 ( 1 - y ) α ⁢ P n ( α , β ) ⁡ ( y ) Γ ⁡ ( α + n + 1 ) ⁢ ( y - x ) μ - 1 Γ ⁡ ( μ ) ⁢ d y , superscript 1 𝑥 𝛼 𝜇 Jacobi-polynomial-P 𝛼 𝜇 𝛽 𝜇 𝑛 𝑥 Euler-Gamma 𝛼 𝜇 𝑛 1 superscript subscript 𝑥 1 superscript 1 𝑦 𝛼 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑦 Euler-Gamma 𝛼 𝑛 1 superscript 𝑦 𝑥 𝜇 1 Euler-Gamma 𝜇 𝑦 {\displaystyle{\displaystyle\frac{(1-x)^{\alpha+\mu}P^{(\alpha+\mu,\beta-\mu)}% _{n}\left(x\right)}{\Gamma\left(\alpha+\mu+n+1\right)}=\int_{x}^{1}\frac{(1-y)% ^{\alpha}P^{(\alpha,\beta)}_{n}\left(y\right)}{\Gamma\left(\alpha+n+1\right)}% \frac{(y-x)^{\mu-1}}{\Gamma\left(\mu\right)}\mathrm{d}y,}}
    0 references
    DLMF id
    DLMF:18.17.E9
    0 references
    constraint
    - 1 < x < 1 1 𝑥 1 {\displaystyle{\displaystyle-1<x<1}}
    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
    Q11660
    Defining formula
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    Q11743
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1ddec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1hdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1fdec
    0 references
     
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