DLMF:17.7.E22 (Q5418): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:17.7.E22	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\sum_{k=-m}^{n}\frac{(1-adp^{k}q^{k})(1-bp^{k}/(dq% ^{k}))}{(1-ad)(1-(b/d))}\frac{\left(a,b;p\right)_{k}\left(c,ad^{2}/(bc);q% \right)_{k}}{\left(dq,adq/b;q\right)_{k}\left(adp/c,bcp/d;p\right)_{k}}q^{k}=% \frac{(1-a)(1-b)(1-c)(1-(ad^{2}/(bc)))}{d(1-ad)(1-(b/d))(1-(c/d))(1-(ad/(bc)))% }\left(\frac{\left(ap,bp;p\right)_{n}\left(cq,ad^{2}q/(bc);q\right)_{n}}{\left% (dq,adq/b;q\right)_{n}\left(adp/c,bcp/d;p\right)_{n}}-\frac{\left(c/(ad),d/(bc% );p\right)_{m+1}\left(1/d,b/(ad);q\right)_{m+1}}{\left(1/c,bc/(ad^{2});q\right% )_{m+1}\left(1/a,1/b;p\right)_{m+1}}\right),}}

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DLMF:17.7.E22

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}

C17.S2.SS1.p1.m6asdec

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Defining formula

{\displaystyle{\displaystyle k}}

C17.S1.XMD1.m1bdec

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Defining formula

{\displaystyle{\displaystyle q}}

C17.S1.XMD10.m1udec

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Defining formula

{\displaystyle{\displaystyle m}}

C17.S1.XMD3.m1bdec

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Defining formula

{\displaystyle{\displaystyle n}}

C17.S1.XMD4.m1jdec

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