DLMF:18.18.E2 (Q5792)

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DLMF:18.18.E2
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    Statements

    Defining formula
    f ⁢ ( z ) = ∑ n = 0 ∞ a n ⁢ P n ( α , β ) ⁡ ( z ) , 𝑓 𝑧 superscript subscript 𝑛 0 subscript 𝑎 𝑛 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑧 {\displaystyle{\displaystyle f(z)=\sum_{n=0}^{\infty}a_{n}P^{(\alpha,\beta)}_{% n}\left(z\right),}}
    0 references
    DLMF id
    DLMF:18.18.E2
    0 references
    Symbols used
    Q11660
    Defining formula
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2aadec
    0 references
    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1dec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1adec
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    Q11762
    Defining formula
    f ⁢ ( z ) 𝑓 𝑧 {\displaystyle{\displaystyle f(z)}}
    xml-id
    C18.S18.XMD1.m1adec
    0 references
     
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