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DLMF:18.22.E24 - MaRDI portal

DLMF:18.22.E24 (Q6591)

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DLMF:18.22.E24
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    Statements

    DLMF defining formula
    ∇ x ( ( β ) x ⁢ c x x ! ⁢ M n ⁡ ( x ; β , c ) ) = ( β - 1 ) x ⁢ c x x ! ⁢ M n + 1 ⁡ ( x ; β - 1 , c ) . backward-difference 𝑥 Pochhammer 𝛽 𝑥 superscript 𝑐 𝑥 𝑥 Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 Pochhammer 𝛽 1 𝑥 superscript 𝑐 𝑥 𝑥 Meixner-polynomial-M 𝑛 1 𝑥 𝛽 1 𝑐 {\displaystyle{\displaystyle\nabla_{x}\left(\frac{{\left(\beta\right)_{x}}c^{x% }}{x!}M_{n}\left(x;\beta,c\right)\right)=\frac{{\left(\beta-1\right)_{x}}c^{x}% }{x!}M_{n+1}\left(x;\beta-1,c\right).}}
    0 references
    Symbols used
    Meixner polynomial
    DLMF defining formula
    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.m2acdec
    0 references
    Q10733
    DLMF defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q11767
    DLMF defining formula
    ∇ x backward-difference 𝑥 {\displaystyle{\displaystyle\nabla_{\NVar{x}}}}
    xml-id
    C18.S1.EGx2.m1abdec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1vdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1wdec
    0 references

    Identifiers

     
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