DLMF:18.9.E19 (Q5615)

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DLMF:18.9.E19
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    Statements

    test
    d d x ⁡ C n ( λ ) ⁡ ( x ) = 2 ⁢ λ ⁢ C n - 1 ( λ + 1 ) ⁡ ( x ) , derivative 𝑥 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 2 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 1 𝑛 1 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}C^{(\lambda)}_{n}% \left(x\right)=2\lambda C^{(\lambda+1)}_{n-1}\left(x\right),}}
    0 references
    DLMF id
    DLMF:18.9.E19
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2addec
    0 references
    Q11475
    test
    C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r3.m2acdec
    0 references
     
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