DLMF:18.26.E6 (Q5936): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11763 / rank
 
Normal rank
Property / Symbols used: Q11763 / qualifier
 
Defining formula:

p n ⁡ ( x ; a , b , a ¯ , missing ) continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 missing {\displaystyle{\displaystyle p_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{\overline{a}},\NVar{missing}\right)\)\@add@PDF@RDFa@triples\end{document}}}

\contHahnpolyp{\NVar{n}}@{\NVar{x}}{\NVar{a}}{\NVar{b}}{\NVar{\conj{a}}}{\NVar% {\conj{b}}}
Property / Symbols used: Q11763 / qualifier
 
xml-id: C18.S19.Px2.p1.m4adec

Revision as of 01:44, 2 January 2020

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DLMF:18.26.E6
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    Statements

    Defining formula
    lim t → ∞ ⁡ W n ⁡ ( ( x + t ) 2 ; a - i ⁢ t , b - i ⁢ t , a ¯ + i ⁢ t , b ¯ + i ⁢ t ) ( - 2 ⁢ t ) n ⁢ n ! = p n ⁡ ( x ; a , b , a ¯ , b ¯ ) . subscript → 𝑡 Wilson-polynomial-W 𝑛 superscript 𝑥 𝑡 2 𝑎 𝑖 𝑡 𝑏 𝑖 𝑡 𝑎 𝑖 𝑡 𝑏 𝑖 𝑡 superscript 2 𝑡 𝑛 𝑛 continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 𝑏 {\displaystyle{\displaystyle\lim_{t\to\infty}\frac{W_{n}\left((x+t)^{2};a-it,b% -it,\overline{a}+it,\overline{b}+it\right)}{(-2t)^{n}n!}=p_{n}\left(x;a,b,% \overline{a},\overline{b}\right).}}
    0 references
    DLMF id
    DLMF:18.26.E6
    0 references
    Symbols used
    Q11783
    Defining formula
    W n ⁡ ( x ; a , b , c , d ) Wilson-polynomial-W 𝑛 𝑥 𝑎 𝑏 𝑐 𝑑 {\displaystyle{\displaystyle W_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{c},\NVar{d}\right)}}
    xml-id
    C18.S25.T1.t1.r2.m2abdec
    0 references
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2adec
    0 references
    Q11763
    Defining formula
    p n ⁡ ( x ; a , b , a ¯ , missing ) continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 missing {\displaystyle{\displaystyle p_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{\overline{a}},\NVar{missing}\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C18.S19.Px2.p1.m4adec
    0 references
     
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