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

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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

Revision as of 12:31, 2 January 2020

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DLMF:18.37.E2
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    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
     
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