DLMF:18.35.E5 (Q6044): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Pollaczek polynomial / rank
 
Normal rank
Property / Symbols used: Pollaczek polynomial / qualifier
 
test:

P n ( λ ) ⁡ ( x ; a , b ) Pollaczek-polynomial-P 𝜆 𝑛 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{a},\NVar{b}\right)}}

\PollaczekpolyP{\NVar{\lambda}}{\NVar{n}}@{\NVar{x}}{\NVar{a}}{\NVar{b}}
Property / Symbols used: Pollaczek polynomial / qualifier
 
xml-id: C18.S35.E4.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec
Property / Symbols used
 
Property / Symbols used: Q11729 / rank
 
Normal rank
Property / Symbols used: Q11729 / qualifier
 
test:

w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}

w(x)
Property / Symbols used: Q11729 / qualifier
 
xml-id: C18.S1.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q11730 / rank
 
Normal rank
Property / Symbols used: Q11730 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11730 / qualifier
 
xml-id: C18.S1.XMD5.m1dec
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.m1bdec
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.m1cdec

Latest revision as of 12:30, 2 January 2020

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DLMF:18.35.E5
No description defined

    Statements

    test
    ∫ - 1 1 P n ( λ ) ⁡ ( x ; a , b ) ⁢ P m ( λ ) ⁡ ( x ; a , b ) ⁢ w ( λ ) ⁢ ( x ; a , b ) ⁢ d x = 0 , superscript subscript 1 1 Pollaczek-polynomial-P 𝜆 𝑛 𝑥 𝑎 𝑏 Pollaczek-polynomial-P 𝜆 𝑚 𝑥 𝑎 𝑏 superscript 𝑤 𝜆 𝑥 𝑎 𝑏 𝑥 0 {\displaystyle{\displaystyle{\int_{-1}^{1}P^{(\lambda)}_{n}\left(x;a,b\right)P% ^{(\lambda)}_{m}\left(x;a,b\right)w^{(\lambda)}(x;a,b)\mathrm{d}x=0},}}
    0 references
    DLMF id
    DLMF:18.35.E5
    0 references
    constraint
    n ≠ m 𝑛 𝑚 {\displaystyle{\displaystyle n\neq m}}
    0 references
    Symbols used
    Pollaczek polynomial
    test
    P n ( λ ) ⁡ ( x ; a , b ) Pollaczek-polynomial-P 𝜆 𝑛 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};% \NVar{a},\NVar{b}\right)}}
    xml-id
    C18.S35.E4.m2acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11729
    test
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1dec
    0 references
    Q11730
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1dec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1bdec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1cdec
    0 references
     
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