DLMF:18.17.E43 (Q5784)

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DLMF:18.17.E43
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    Defining formula
    ⨍ - 1 1 U n - 1 ⁡ ( y ) ⁢ ( 1 - y 2 ) 1 2 y - x ⁢ d y = - π ⁢ T n ⁡ ( x ) . superscript subscript principal-value-integral 1 1 Chebyshev-polynomial-second-kind-U 𝑛 1 𝑦 superscript 1 superscript 𝑦 2 1 2 𝑦 𝑥 𝑦 𝜋 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle\pvint_{-1}^{1}U_{n-1}\left(y\right)\frac{(1-y^{2}% )^{\frac{1}{2}}}{y-x}\mathrm{d}y=-\pi T_{n}\left(x\right).}}
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    DLMF id
    DLMF:18.17.E43
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