DLMF:18.23.E4 (Q5905): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11663 / rank
 
Normal rank
Property / Symbols used: Q11663 / qualifier
 
test:

M n ⁡ ( x ; β , c ) Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 {\displaystyle{\displaystyle M_{\NVar{n}}\left(\NVar{x};\NVar{\beta},\NVar{c}% \right)}}

\MeixnerpolyM{\NVar{n}}@{\NVar{x}}{\NVar{\beta}}{\NVar{c}}
Property / Symbols used: Q11663 / qualifier
 
xml-id: C18.S19.T1.t1.r4.m2adec
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1abdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec
Property / Symbols used
 
Property / Symbols used: Q11750 / rank
 
Normal rank
Property / Symbols used: Q11750 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11750 / qualifier
 
xml-id: C18.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1cdec

Latest revision as of 00:39, 2 January 2020

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English
DLMF:18.23.E4
No description defined

    Statements

    test
    ( 1 - z c ) x ⁢ ( 1 - z ) - x - β = ∑ n = 0 ∞ ( β ) n n ! ⁢ M n ⁡ ( x ; β , c ) ⁢ z n , superscript 1 𝑧 𝑐 𝑥 superscript 1 𝑧 𝑥 𝛽 superscript subscript 𝑛 0 Pochhammer 𝛽 𝑛 𝑛 Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\left(1-\frac{z}{c}\right)^{x}(1-z)^{-x-\beta}=% \sum_{n=0}^{\infty}\frac{{\left(\beta\right)_{n}}}{n!}M_{n}\left(x;\beta,c% \right)z^{n},}}
    0 references
    DLMF id
    DLMF:18.23.E4
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    Q11663
    test
    M n ⁡ ( x ; β , c ) Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 {\displaystyle{\displaystyle M_{\NVar{n}}\left(\NVar{x};\NVar{\beta},\NVar{c}% \right)}}
    xml-id
    C18.S19.T1.t1.r4.m2adec
    0 references
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    Q11750
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1cdec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1cdec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1cdec
    0 references
     
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