DLMF:18.37.E4 (Q6052): 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.m2acdec

Revision as of 12:32, 2 January 2020

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DLMF:18.37.E4
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    Statements

    test
    ∬ x 2 + y 2 < 1 R m , n ( α ) ⁡ ( x + i ⁢ y ) ⁢ ( x - i ⁢ y ) m - j ⁢ ( x + i ⁢ y ) n - j ⁢ ( 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 superscript 𝑥 𝑖 𝑦 𝑚 𝑗 superscript 𝑥 𝑖 𝑦 𝑛 𝑗 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)(x-iy)^{m-j}(x+iy)^{n-j}\*(1-x^{2}-y^{2})^{\alpha}% \mathrm{d}x\mathrm{d}y=0,}}
    0 references
    DLMF id
    DLMF:18.37.E4
    0 references
    constraint
    j = 1 , 2 , … , min ⁡ ( m , n ) 𝑗 1 2 … 𝑚 𝑛 {\displaystyle{\displaystyle j=1,2,\dots,\min(m,n)}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    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.m2acdec
    0 references
     
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