Formula:KLS:01.15:17

<< Formula:KLS:01.15:16

formula in The q-derivative and q-integral

The q-derivative and q-integral >>

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}{q}{\infty}}{\qPochhammer{dt,et}{q}{\infty}}\,d_qt =(b-a)(1-q)\,\frac{\qPochhammer{q,a^{-1}bq,ab^{-1}q,abde}{q}{\infty}}{\qPochhammer{ad,ae,bd,be}{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

Bibliography

Equation in Section 1.15 of KLS.

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<< Formula:KLS:01.15:16

formula in The q-derivative and q-integral

The q-derivative and q-integral >>