DLMF:18.1.E2 (Q5487): 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.m1adec

Revision as of 15:12, 2 January 2020

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DLMF:18.1.E2
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    Statements

    Defining formula
    G n ⁡ ( p , q , x ) = n ! ( n + p ) n ⁢ P n ( p - q , q - 1 ) ⁡ ( 2 ⁢ x - 1 ) , shifted-Jacobi-polynomial-G 𝑛 𝑝 𝑞 𝑥 𝑛 Pochhammer 𝑛 𝑝 𝑛 Jacobi-polynomial-P 𝑝 𝑞 𝑞 1 𝑛 2 𝑥 1 {\displaystyle{\displaystyle G_{n}\left(p,q,x\right)=\frac{n!}{{\left(n+p% \right)_{n}}}P^{(p-q,q-1)}_{n}\left(2x-1\right),}}
    0 references
    DLMF id
    DLMF:18.1.E2
    0 references
    Symbols used
    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
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q11728
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C18.S1.XMD3.m1dec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1adec
    0 references
     
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