DLMF:18.34.E8 (Q6038): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11660 / rank
 
Normal rank
Property / Symbols used: Q11660 / qualifier
 
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)}}

\JacobipolyP{\NVar{\alpha}}{\NVar{\beta}}{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11660 / qualifier
 
xml-id: C18.S3.T1.t1.r2.m2adec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1edec

Latest revision as of 13:29, 2 January 2020

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English
DLMF:18.34.E8
No description defined

    Statements

    Defining formula
    lim α → ∞ ⁡ P n ( α , a - α - 2 ) ⁡ ( 1 + α ⁢ x ) P n ( α , a - α - 2 ) ⁡ ( 1 ) = y n ⁡ ( x ; a ) . subscript → 𝛼 Jacobi-polynomial-P 𝛼 𝑎 𝛼 2 𝑛 1 𝛼 𝑥 Jacobi-polynomial-P 𝛼 𝑎 𝛼 2 𝑛 1 Bessel-polynomial-y 𝑛 𝑥 𝑎 {\displaystyle{\displaystyle\lim_{\alpha\to\infty}\frac{P^{(\alpha,a-\alpha-2)% }_{n}\left(1+\alpha x\right)}{P^{(\alpha,a-\alpha-2)}_{n}\left(1\right)}=y_{n}% \left(x;a\right).}}
    0 references
    DLMF id
    DLMF:18.34.E8
    0 references
    Symbols used
    Bessel polynomial
    Defining formula
    y n ⁡ ( x ; a ) Bessel-polynomial-y 𝑛 𝑥 𝑎 {\displaystyle{\displaystyle y_{\NVar{n}}\left(\NVar{x};\NVar{a}\right)}}
    xml-id
    C18.S34.E1.m2afdec
    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.m1gdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1edec
    0 references
     
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