DLMF:18.9.E19 (Q5615): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1sdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1rdec

Latest revision as of 15:24, 2 January 2020

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DLMF:18.9.E19
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    Statements

    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),}}
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    DLMF:18.9.E19
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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.m2addec
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    C n ( λ ) ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    C18.S3.T1.t1.r3.m2acdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1sdec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1rdec
    0 references