DLMF:18.37.E2 (Q6050): Difference between revisions

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Property / constraint
 

n ≠ ℓ 𝑛 ℓ {\displaystyle{\displaystyle n\neq\ell}}

n\neq\ell
Property / constraint: n ≠ ℓ 𝑛 ℓ {\displaystyle{\displaystyle n\neq\ell}} / rank
 
Normal rank
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: disk polynomial / rank
 
Normal rank
Property / Symbols used: disk polynomial / qualifier
 
test:

R m , n ( α ) ⁡ ( z ) disk-orthogonal-polynomial-R 𝛼 𝑚 𝑛 𝑧 {\displaystyle{\displaystyle R^{(\NVar{\alpha})}_{\NVar{m},\NVar{n}}\left(% \NVar{z}\right)}}

\diskpoly{\NVar{\alpha}}{\NVar{m}}{\NVar{n}}@{\NVar{z}}
Property / Symbols used: disk polynomial / qualifier
 
xml-id: C18.S37.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11743 / rank
 
Normal rank
Property / Symbols used: Q11743 / qualifier
 
test:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11743 / qualifier
 
xml-id: C18.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11744 / rank
 
Normal rank
Property / Symbols used: Q11744 / qualifier
 
test:

ℓ ℓ {\displaystyle{\displaystyle\ell}}

\ell
Property / Symbols used: Q11744 / qualifier
 
xml-id: C18.S1.XMD4.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.m1adec
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.m1adec
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.m1dec

Latest revision as of 12:31, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.37.E2
No description defined

    Statements

    test
    ∬ x 2 + y 2 < 1 R m , n ( α ) ⁡ ( x + i ⁢ y ) ⁢ R j , ℓ ( α ) ⁡ ( x - i ⁢ y ) ⁢ ( 1 - x 2 - y 2 ) α ⁢ d x ⁢ d y = 0 , subscript double-integral superscript 𝑥 2 superscript 𝑦 2 1 disk-orthogonal-polynomial-R 𝛼 𝑚 𝑛 𝑥 imaginary-unit 𝑦 disk-orthogonal-polynomial-R 𝛼 𝑗 ℓ 𝑥 imaginary-unit 𝑦 superscript 1 superscript 𝑥 2 superscript 𝑦 2 𝛼 𝑥 𝑦 0 {\displaystyle{\displaystyle\iint\limits_{x^{2}+y^{2}<1}R^{(\alpha)}_{m,n}% \left(x+\mathrm{i}y\right)R^{(\alpha)}_{j,\ell}\left(x-\mathrm{i}y\right)\*(1-% x^{2}-y^{2})^{\alpha}\mathrm{d}x\mathrm{d}y=0,}}
    0 references
    DLMF id
    DLMF:18.37.E2
    0 references
    constraint
    n ≠ ℓ 𝑛 ℓ {\displaystyle{\displaystyle n\neq\ell}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    disk polynomial
    test
    R m , n ( α ) ⁡ ( z ) disk-orthogonal-polynomial-R 𝛼 𝑚 𝑛 𝑧 {\displaystyle{\displaystyle R^{(\NVar{\alpha})}_{\NVar{m},\NVar{n}}\left(% \NVar{z}\right)}}
    xml-id
    C18.S37.E1.m2aadec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q11743
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1dec
    0 references
    Q11744
    test
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C18.S1.XMD4.m1dec
    0 references
    Q11730
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1adec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1adec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1dec
    0 references
     
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