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

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Property / Symbols used
 
Property / Symbols used: Bessel polynomial / rank
 
Normal rank
Property / Symbols used: Bessel polynomial / qualifier
 
Defining formula:

y n ⁡ ( x ; a ) Bessel-polynomial-y 𝑛 𝑥 𝑎 {\displaystyle{\displaystyle y_{\NVar{n}}\left(\NVar{x};\NVar{a}\right)}}

\Besselpolyy{\NVar{n}}@{\NVar{x}}{\NVar{a}}
Property / Symbols used: Bessel polynomial / qualifier
 
xml-id: C18.S34.E1.m2afdec

Revision as of 13:29, 2 January 2020

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DLMF:18.34.E8
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    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
     
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