DLMF:3.11.E8 (Q1449)

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DLMF:3.11.E8
No description defined

    Statements

    Defining formula
    ∫ - 1 1 T j ⁡ ( x ) ⁢ T k ⁡ ( x ) 1 - x 2 ⁢ d x = { π , j = k = 0 , 1 2 ⁢ π , j = k ≠ 0 , 0 , j ≠ k , superscript subscript 1 1 Chebyshev-polynomial-first-kind-T 𝑗 𝑥 Chebyshev-polynomial-first-kind-T 𝑘 𝑥 1 superscript 𝑥 2 𝑥 cases 𝑗 𝑘 0 1 2 𝑗 𝑘 0 0 𝑗 𝑘 {\displaystyle{\displaystyle\int_{-1}^{1}\frac{T_{j}\left(x\right)T_{k}\left(x% \right)}{\sqrt{1-x^{2}}}\mathrm{d}x=\begin{cases}\pi,&j=k=0,\\ \frac{1}{2}\pi,&j=k\neq 0,\\ 0,&j\neq k,\end{cases}}}
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    DLMF id
    DLMF:3.11.E8
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    Symbols used
    Q11207
    Defining formula
    T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r4.m2abdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
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