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DLMF:18.26.E13 - MaRDI portal

DLMF:18.26.E13 (Q6639)

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DLMF:18.26.E13
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    Statements

    DLMF defining formula
    lim N → ∞ ⁡ R n ⁡ ( r ⁢ ( x ; β , c , N ) ; β - 1 , c - 1 ⁢ ( 1 - c ) ⁢ N , N ) = M n ⁡ ( x ; β , c ) . subscript → 𝑁 dual-Hahn-R 𝑛 𝑟 𝑥 𝛽 𝑐 𝑁 𝛽 1 superscript 𝑐 1 1 𝑐 𝑁 𝑁 Meixner-polynomial-M 𝑛 𝑥 𝛽 𝑐 {\displaystyle{\displaystyle\lim_{N\to\infty}R_{n}\left(r(x;\beta,c,N);\beta-1% ,c^{-1}(1-c)N,N\right)=M_{n}\left(x;\beta,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.m2adec
    0 references
    dual Hahn polynomial
    DLMF defining formula
    R n ⁡ ( x ; γ , δ , N ) dual-Hahn-R 𝑛 𝑥 𝛾 𝛿 𝑁 {\displaystyle{\displaystyle R_{\NVar{n}}\left(\NVar{x};\NVar{\gamma},\NVar{% \delta},\NVar{N}\right)}}
    xml-id
    C18.S25.T1.t1.r5.m2acdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1kdec
    0 references
    positive integer
    DLMF defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1fdec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1hdec
    0 references
    18.26.E12
    DLMF defining formula
    r ⁢ ( x ; β , c , N ) 𝑟 𝑥 𝛽 𝑐 𝑁 {\displaystyle{\displaystyle r(x;\beta,c,N)}}
    xml-id
    C18.S26.XMD1.m1adec
    0 references

    Identifiers

     
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