DLMF:15.9.E6 (Q5096)

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DLMF:15.9.E6
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    Statements

    Defining formula
    U n ⁡ ( x ) = ( n + 1 ) ⁢ F ⁡ ( - n , n + 2 3 2 ; 1 - x 2 ) . Chebyshev-polynomial-second-kind-U 𝑛 𝑥 𝑛 1 Gauss-hypergeometric-F 𝑛 𝑛 2 3 2 1 𝑥 2 {\displaystyle{\displaystyle U_{n}\left(x\right)=(n+1)F\left({-n,n+2\atop\frac% {3}{2}};\frac{1-x}{2}\right).}}
    0 references
    DLMF id
    DLMF:15.9.E6
    0 references
    Symbols used
    Q11661
    Defining formula
    U n ⁡ ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r5.m2adec
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    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    Defining formula
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2aedec
    0 references
    Q11649
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C15.S1.XMD1.m1ddec
    0 references
    Q11650
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C15.S1.XMD10.m1edec
    0 references
     
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