DLMF:18.22.E20 (Q5891): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11764 / rank
 
Normal rank
Property / Symbols used: Q11764 / qualifier
 
Defining formula:

∇ x backward-difference 𝑥 {\displaystyle{\displaystyle\nabla_{\NVar{x}}}}

\bDiff[\NVar{x}]
Property / Symbols used: Q11764 / qualifier
 
xml-id: C18.S1.EGx2.m1adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
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.m1rdec
Property / Symbols used
 
Property / Symbols used: Q11736 / rank
 
Normal rank
Property / Symbols used: Q11736 / qualifier
 
Defining formula:

N 𝑁 {\displaystyle{\displaystyle N}}

N
Property / Symbols used: Q11736 / qualifier
 
xml-id: C18.S1.XMD7.m1gdec
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.m1sdec

Latest revision as of 01:36, 2 January 2020

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DLMF:18.22.E20
No description defined

    Statements

    Defining formula
    ∇ x ( ( α + 1 ) x ⁢ ( β + 1 ) N - x x ! ⁢ ( N - x ) ! ⁢ Q n ⁡ ( x ; α , β , N ) ) = N + 1 β ⁢ ( α ) x ⁢ ( β ) N + 1 - x x ! ⁢ ( N + 1 - x ) ! ⁢ Q n + 1 ⁡ ( x ; α - 1 , β - 1 , N + 1 ) . backward-difference 𝑥 Pochhammer 𝛼 1 𝑥 Pochhammer 𝛽 1 𝑁 𝑥 𝑥 𝑁 𝑥 Hahn-polynomial-Q 𝑛 𝑥 𝛼 𝛽 𝑁 𝑁 1 𝛽 Pochhammer 𝛼 𝑥 Pochhammer 𝛽 𝑁 1 𝑥 𝑥 𝑁 1 𝑥 Hahn-polynomial-Q 𝑛 1 𝑥 𝛼 1 𝛽 1 𝑁 1 {\displaystyle{\displaystyle\nabla_{x}\left(\frac{{\left(\alpha+1\right)_{x}}{% \left(\beta+1\right)_{N-x}}}{x!\;(N-x)!}Q_{n}\left(x;\alpha,\beta,N\right)% \right)=\frac{N+1}{\beta}\frac{{\left(\alpha\right)_{x}}{\left(\beta\right)_{N% +1-x}}}{x!\;(N+1-x)!}\*Q_{n+1}\left(x;\alpha-1,\beta-1,N+1\right).}}
    0 references
    DLMF id
    DLMF:18.22.E20
    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.m1acdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q11764
    Defining formula
    ∇ x backward-difference 𝑥 {\displaystyle{\displaystyle\nabla_{\NVar{x}}}}
    xml-id
    C18.S1.EGx2.m1adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1rdec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1gdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1sdec
    0 references
     
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