DLMF:18.17.E46 (Q5787)

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DLMF:18.17.E46
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    test
    ( n + 1 2 ) ⁢ ( 1 - x ) 1 2 ⁢ ∫ x 1 ( t - x ) - 1 2 ⁢ P n ⁡ ( t ) ⁢ d t = T n ⁡ ( x ) - T n + 1 ⁡ ( x ) . 𝑛 1 2 superscript 1 𝑥 1 2 superscript subscript 𝑥 1 superscript 𝑡 𝑥 1 2 Legendre-spherical-polynomial 𝑛 𝑡 𝑡 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 Chebyshev-polynomial-first-kind-T 𝑛 1 𝑥 {\displaystyle{\displaystyle(n+\tfrac{1}{2})(1-x)^{\frac{1}{2}}\int_{x}^{1}(t-% x)^{-\frac{1}{2}}P_{n}\left(t\right)\mathrm{d}t=T_{n}\left(x\right)-T_{n+1}% \left(x\right).}}
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    DLMF id
    DLMF:18.17.E46
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