DLMF:18.37.E6 (Q6054): Difference between revisions

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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.m1edec

Latest revision as of 13:32, 2 January 2020

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DLMF:18.37.E6
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    Statements

    Defining formula
    R m , n ( α ) ⁡ ( z ) = ∑ j = 0 min ⁡ ( m , n ) ( - 1 ) j ⁢ ( α + 1 ) m + n - j ⁢ ( - m ) j ⁢ ( - n ) j ( α + 1 ) m ⁢ ( α + 1 ) n ⁢ j ! ⁢ z m - j ⁢ z ¯ n - j . disk-orthogonal-polynomial-R 𝛼 𝑚 𝑛 𝑧 superscript subscript 𝑗 0 𝑚 𝑛 superscript 1 𝑗 Pochhammer 𝛼 1 𝑚 𝑛 𝑗 Pochhammer 𝑚 𝑗 Pochhammer 𝑛 𝑗 Pochhammer 𝛼 1 𝑚 Pochhammer 𝛼 1 𝑛 𝑗 superscript 𝑧 𝑚 𝑗 𝑧 𝑛 𝑗 {\displaystyle{\displaystyle R^{(\alpha)}_{m,n}\left(z\right)=\sum_{j=0}^{\min% (m,n)}\frac{(-1)^{j}{\left(\alpha+1\right)_{m+n-j}}{\left(-m\right)_{j}}{\left% (-n\right)_{j}}}{{\left(\alpha+1\right)_{m}}{\left(\alpha+1\right)_{n}}j!}\*z^% {m-j}\*{\overline{z}^{n-j}}.}}
    0 references
    DLMF id
    DLMF:18.37.E6
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2aadec
    0 references
    disk polynomial
    Defining formula
    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.m2aedec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1bdec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1edec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
    0 references
     
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