Formula:KLS:01.15:16

<< Formula:KLS:01.15:15

formula in The q-derivative and q-integral

Formula:KLS:01.15:17 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int_a^b\frac{\qPochhammer{a^{-1}qt,b^{-1}qt,ct}{q}{\infty}}{\qPochhammer{dt,et,ft}{q}{\infty}}\,d_qt {}=(b-a)(1-q)\,\frac{\qPochhammer{q,a^{-1}bq,ab^{-1}q,cd^{-1},c\expe^{-1},cf^{-1}}{q}{\infty}} {\qPochhammer{ad,ae,af,bd,be,bf}{q}{\infty}} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int}}  : integral : http://dlmf.nist.gov/1.4#iv
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a;q)_n}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \mathrm{e}}}  : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11

Bibliography

Equation in Section 1.15 of KLS.

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<< Formula:KLS:01.15:15

formula in The q-derivative and q-integral

Formula:KLS:01.15:17 >>