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Formula:KLS:01.13:03 - Revision history
2024-03-29T11:32:25Z
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imported>SeedBot: DRMF
2017-03-05T22:34:36Z
<p>DRMF</p>
<p><b>New page</b></p><div>{{DISPLAYTITLE:Formula:KLS:01.13:03}}<br />
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<div id="alignleft"> << [[Formula:KLS:01.13:02|Formula:KLS:01.13:02]] </div><br />
<div id="aligncenter"> [[Transformation_formulas#KLS:01.13:03|formula in Transformation formulas]] </div><br />
<div id="alignright"> [[Formula:KLS:01.13:04|Formula:KLS:01.13:04]] >> </div><br />
</div><br />
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<br /><div align="center"><math>{\displaystyle <br />
\index{Heine's transformation formula}\index{Transformation formula!Heine}<br />
\qHyperrphis{2}{1}@@{a,b}{c}{q}{z}=\frac{\qPochhammer{abc^{-1}z}{q}{\infty}}{\qPochhammer{z}{q}{\infty}}\<br />
\qHyperrphis{2}{1}@@{a^{-1}c,b^{-1}c}{c}{q}{\frac{abz}{c}}.\label{Heine3}<br />
}</math></div><br />
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== Proof ==<br />
<br />
We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.<br />
<br />
== Symbols List ==<br />
<br />
<span class="plainlinks">[http://dlmf.nist.gov/17.4#E1 <math>{\displaystyle {{}_{r}\phi_{s}}}</math>]</span> : basic hypergeometric (or <math>{\displaystyle q}</math>-hypergeometric) function : [http://dlmf.nist.gov/17.4#E1 http://dlmf.nist.gov/17.4#E1]<br /><br />
<span class="plainlinks">[http://dlmf.nist.gov/5.18#i <math>{\displaystyle (a;q)_n}</math>]</span> : <math>{\displaystyle q}</math>-Pochhammer symbol : [http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/5.18#i] [http://dlmf.nist.gov/17.2#SS1.p1 http://dlmf.nist.gov/17.2#SS1.p1]<br />
<br /><br />
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== Bibliography==<br />
<br />
<span class="plainlinks">[http://homepage.tudelft.nl/11r49/askey/contents.html Equation in Section 1.13]</span> of [[Bibliography#KLS|'''KLS''']].<br />
<br />
== URL links ==<br />
<br />
We ask users to provide relevant URL links in this space.<br />
<br />
<br /><div id="drmf_foot"><br />
<div id="alignleft"> << [[Formula:KLS:01.13:02|Formula:KLS:01.13:02]] </div><br />
<div id="aligncenter"> [[Transformation_formulas#KLS:01.13:03|formula in Transformation formulas]] </div><br />
<div id="alignright"> [[Formula:KLS:01.13:04|Formula:KLS:01.13:04]] >> </div><br />
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