DLMF:18.21.E5 (Q5859)

From DRMF
Revision as of 01:33, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:18.21.E5
No description defined

    Statements

    Defining formula
    lim N → ∞ ⁡ Q n ⁡ ( N ⁢ x ; α , β , N ) = P n ( α , β ) ⁡ ( 1 - 2 ⁢ x ) P n ( α , β ) ⁡ ( 1 ) . subscript → 𝑁 Hahn-polynomial-Q 𝑛 𝑁 𝑥 𝛼 𝛽 𝑁 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 2 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 {\displaystyle{\displaystyle\lim_{N\to\infty}Q_{n}\left(Nx;\alpha,\beta,N% \right)=\frac{P^{(\alpha,\beta)}_{n}\left(1-2x\right)}{P^{(\alpha,\beta)}_{n}% \left(1\right)}.}}
    0 references
    DLMF id
    DLMF:18.21.E5
    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
    Q11660
    Defining formula
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ddec
    0 references
    Q11736
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C18.S1.XMD7.m1ddec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1ddec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5859&oldid=32479"