DLMF:18.20.E3 (Q5844): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11767 / rank
 
Normal rank
Property / Symbols used: Q11767 / qualifier
 
Defining formula:

δ x central-difference 𝑥 {\displaystyle{\displaystyle\delta_{\NVar{x}}}}

\cDiff[\NVar{x}]
Property / Symbols used: Q11767 / qualifier
 
xml-id: C18.S1.EGx3.m1adec
Property / Symbols used
 
Property / Symbols used: complex conjugate / rank
 
Normal rank
Property / Symbols used: complex conjugate / qualifier
 
Defining formula:

z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}

\conj{\NVar{z}}
Property / Symbols used: complex conjugate / qualifier
 
xml-id: C1.S9.E11.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.m4adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
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.m1cdec
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.m1cdec

Latest revision as of 01:31, 2 January 2020

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Language Label Description Also known as
English
DLMF:18.20.E3
No description defined

    Statements

    Defining formula
    w ⁢ ( x ; a , b , a ¯ , b ¯ ) ⁢ p n ⁡ ( x ; a , b , a ¯ , b ¯ ) = 1 n ! ⁢ δ x n ( w ⁢ ( x ; a + 1 2 ⁢ n , b + 1 2 ⁢ n , a ¯ + 1 2 ⁢ n , b ¯ + 1 2 ⁢ n ) ) . 𝑤 𝑥 𝑎 𝑏 𝑎 𝑏 continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 𝑏 1 𝑛 superscript central-difference 𝑥 𝑛 𝑤 𝑥 𝑎 1 2 𝑛 𝑏 1 2 𝑛 𝑎 1 2 𝑛 𝑏 1 2 𝑛 {\displaystyle{\displaystyle w(x;a,b,\overline{a},\overline{b})p_{n}\left(x;a,% b,\overline{a},\overline{b}\right)=\frac{1}{n!}\delta_{x}^{n}\left(w(x;a+% \tfrac{1}{2}n,b+\tfrac{1}{2}n,\overline{a}+\tfrac{1}{2}n,\overline{b}+\tfrac{1% }{2}n)\right).}}
    0 references
    DLMF id
    DLMF:18.20.E3
    0 references
    Symbols used
    Q11767
    Defining formula
    δ x central-difference 𝑥 {\displaystyle{\displaystyle\delta_{\NVar{x}}}}
    xml-id
    C18.S1.EGx3.m1adec
    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
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1cdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1cdec
    0 references
     
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