Formula:KLS:01.15:07

<< Formula:KLS:01.15:06

formula in The q-derivative and q-integral

Formula:KLS:01.15:08 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \qderiv[n]{q}@{f(x)g(x)}=\sum_{k=0}^n\qBinomial{n}{k}{q} \left(\qderiv[n-k]{q}f\right)(q^kx)\left(\qderiv[k]{q}g\right)(x) }}

Constraint(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle n=0,1,2,\ldots}}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathcal{D}_q^n}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -derivative : http://drmf.wmflabs.org/wiki/Definition:qderiv
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \genfrac[]\z@{}{n}{j}_{q}}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -binomial coefficient (or Gaussian polynomial) : http://dlmf.nist.gov/17.2#E27 http://dlmf.nist.gov/26.9#SS2.p1

Bibliography

Equation in Section 1.15 of KLS.

URL links

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<< Formula:KLS:01.15:06

formula in The q-derivative and q-integral

Formula:KLS:01.15:08 >>