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DLMF:18.6.E2 - MaRDI portal

DLMF:18.6.E2 (Q6262)

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DLMF:18.6.E2
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    Statements

    DLMF defining formula
    lim α → ∞ ⁡ P n ( α , β ) ⁡ ( x ) P n ( α , β ) ⁡ ( 1 ) = ( 1 + x 2 ) n , subscript → 𝛼 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 superscript 1 𝑥 2 𝑛 {\displaystyle{\displaystyle\lim_{\alpha\to\infty}\frac{P^{(\alpha,\beta)}_{n}% \left(x\right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}=\left(\frac{1+x}{2}% \right)^{n},}}
    0 references
    Symbols used
    Jacobi polynomial
    DLMF 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.m2aadec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1bdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1adec
    0 references

    Identifiers

     
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