DLMF:18.7.E22 (Q5590): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11660 / rank
 
Normal rank
Property / Symbols used: Q11660 / qualifier
 
test:

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.m2aldec
Property / Symbols used
 
Property / Symbols used: Q11333 / rank
 
Normal rank
Property / Symbols used: Q11333 / qualifier
 
test:

L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}

\LaguerrepolyL[\NVar{\alpha}]{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11333 / qualifier
 
xml-id: C18.S3.T1.t1.r12.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1udec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1udec

Latest revision as of 14:21, 2 January 2020

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DLMF:18.7.E22
No description defined

    Statements

    test
    lim α → ∞ ⁡ P n ( α , β ) ⁡ ( ( 2 ⁢ x / α ) - 1 ) = ( - 1 ) n ⁢ L n ( β ) ⁡ ( x ) . subscript → 𝛼 Jacobi-polynomial-P 𝛼 𝛽 𝑛 2 𝑥 𝛼 1 superscript 1 𝑛 Laguerre-polynomial-L 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle\lim_{\alpha\to\infty}P^{(\alpha,\beta)}_{n}\left(% (2x/\alpha)-1\right)=(-1)^{n}L^{(\beta)}_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.7.E22
    0 references
    Symbols used
    Q11660
    test
    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.m2aldec
    0 references
    Q11333
    test
    L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r12.m2acdec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1udec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1udec
    0 references
     
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