DLMF:18.22.E19 (Q5890): Difference between revisions

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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.m1rdec

Latest revision as of 01:36, 2 January 2020

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DLMF:18.22.E19
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    Statements

    Defining formula
    Δ x Q n ⁡ ( x ; α , β , N ) = - n ⁢ ( n + α + β + 1 ) ( α + 1 ) ⁢ N ⁢ Q n - 1 ⁡ ( x ; α + 1 , β + 1 , N - 1 ) , forward-difference 𝑥 Hahn-polynomial-Q 𝑛 𝑥 𝛼 𝛽 𝑁 𝑛 𝑛 𝛼 𝛽 1 𝛼 1 𝑁 Hahn-polynomial-Q 𝑛 1 𝑥 𝛼 1 𝛽 1 𝑁 1 {\displaystyle{\displaystyle\Delta_{x}Q_{n}\left(x;\alpha,\beta,N\right)=-% \frac{n(n+\alpha+\beta+1)}{(\alpha+1)N}Q_{n-1}\left(x;\alpha+1,\beta+1,N-1% \right),}}
    0 references
    DLMF id
    DLMF:18.22.E19
    0 references
    Symbols used
    Q11768
    Defining formula
    Q n ⁡ ( x ; α , β , N ) Hahn-polynomial-Q 𝑛 𝑥 𝛼 𝛽 𝑁 {\displaystyle{\displaystyle Q_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{% \beta},\NVar{N}\right)}}
    xml-id
    C18.S19.T1.t1.r2.m1abdec
    0 references
    Q11097
    Defining formula
    Δ forward-difference {\displaystyle{\displaystyle\Delta}}
    xml-id
    C3.S6.SS1.p1.m2adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1qdec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1fdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1rdec
    0 references
     
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