DLMF:18.21.E11 (Q5865): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11664 / rank
 
Normal rank
Property / Symbols used: Q11664 / qualifier
 
Defining formula:

P n ( λ ) ⁡ ( x ; ϕ ) Meixner-Pollaczek-polynomial-P 𝜆 𝑛 𝑥 italic-ϕ {\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{\phi}\right)}}

\MeixnerPollaczekpolyP{\NVar{\lambda}}{\NVar{n}}@{\NVar{x}}{\NVar{\phi}}
Property / Symbols used: Q11664 / qualifier
 
xml-id: C18.S19.Px3.p1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
Defining formula:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1adec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2adec
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.m4aadec
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.m1jdec
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.m1jdec

Latest revision as of 01:34, 2 January 2020

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Language Label Description Also known as
English
DLMF:18.21.E11
No description defined

    Statements

    Defining formula
    p n ⁡ ( x ; a , a + 1 2 , a , a + 1 2 ) = 2 - 2 ⁢ n ⁢ ( 4 ⁢ a + n ) n ⁢ P n ( 2 ⁢ a ) ⁡ ( 2 ⁢ x ; 1 2 ⁢ π ) . continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑎 1 2 𝑎 𝑎 1 2 superscript 2 2 𝑛 Pochhammer 4 𝑎 𝑛 𝑛 Meixner-Pollaczek-polynomial-P 2 𝑎 𝑛 2 𝑥 1 2 𝜋 {\displaystyle{\displaystyle p_{n}\left(x;a,a+\tfrac{1}{2},a,a+\tfrac{1}{2}% \right)=2^{-2n}{\left(4a+n\right)_{n}}P^{(2a)}_{n}\left(2x;\tfrac{1}{2}\pi% \right).}}
    0 references
    DLMF id
    DLMF:18.21.E11
    0 references
    Symbols used
    Q11664
    Defining formula
    P n ( λ ) ⁡ ( x ; ϕ ) Meixner-Pollaczek-polynomial-P 𝜆 𝑛 𝑥 italic-ϕ {\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{\phi}\right)}}
    xml-id
    C18.S19.Px3.p1.m2aadec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.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.m4aadec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1jdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1jdec
    0 references
     
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