DLMF:18.9.E20 (Q5616): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2aedec

Revision as of 14:24, 2 January 2020

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DLMF:18.9.E20
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    Statements

    d d x ( ( 1 - x 2 ) λ - 1 2 C n ( λ ) ( x ) ) = - ( n + 1 ) ( n + 2 λ - 1 ) 2 ( λ - 1 ) ( 1 - x 2 ) λ - 3 2 C n + 1 ( λ - 1 ) ( x ) . derivative 𝑥 superscript 1 superscript 𝑥 2 𝜆 1 2 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 𝑛 1 𝑛 2 𝜆 1 2 𝜆 1 superscript 1 superscript 𝑥 2 𝜆 3 2 ultraspherical-Gegenbauer-polynomial 𝜆 1 𝑛 1 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}\left((1-x^{2})^{% \lambda-\frac{1}{2}}C^{(\lambda)}_{n}\left(x\right)\right)=-\frac{(n+1)(n+2% \lambda-1)}{2(\lambda-1)}{(1-x^{2})^{\lambda-\frac{3}{2}}}C^{(\lambda-1)}_{n+1% }\left(x\right).}}
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    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2aedec
    0 references