Definition:monicbigqLegendre and Definition:qHahn: Difference between pages
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<div id="drmf_head"> | <div id="drmf_head"> | ||
<div id="alignleft"> << [[Definition: | <div id="alignleft"> << [[Definition:normctsqHahnptilde|Definition:normctsqHahnptilde]] </div> | ||
<div id="aligncenter"> [[Main_Page|Main Page]] </div> | <div id="aligncenter"> [[Main_Page|Main Page]] </div> | ||
<div id="alignright"> [[Definition: | <div id="alignright"> [[Definition:AlSalamChihara|Definition:AlSalamChihara]] >> </div> | ||
</div> | </div> | ||
The LaTeX DLMF and DRMF macro '''\ | The LaTeX DLMF and DRMF macro '''\qHahn''' represents the <math>q</math>-Hahn polynomial. | ||
This macro is in the category of polynomials. | This macro is in the category of polynomials. | ||
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In math mode, this macro can be called in the following ways: | In math mode, this macro can be called in the following ways: | ||
:'''\ | :'''\qHahn{n}@{q^{-x}}{\alpha}{\beta}{N}''' produces <math>{\displaystyle \qHahn{n}@{q^{-x}}{\alpha}{\beta}{N}}</math><br /> | ||
:'''\qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N}''' produces <math>{\displaystyle \qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N}}</math><br /> | |||
:'''\ | |||
These are defined by | These are defined by <ref>[[Formula:KLS:01.10:11]]</ref> | ||
<math> | |||
<math display=block> | |||
\qHahn{N}@{q^{-x}}{\alpha}{\beta}{N}{q}=\sum_{k=0}^N | |||
\frac{\qPochhammer{\alpha\beta q^{N+1}}{q}{k}\qPochhammer{q^{-x}}{q}{k}}{\qPochhammer{\alpha q}{q}{k}\qPochhammer{q}{q}{k}}q^k | |||
</math> | |||
or <ref>[[Formula:KLS:14.06:01]]</ref> | |||
<math>{\displaystyle | |||
\qHahn{n}@{q^{-x}}{\alpha}{\beta}{N}{q}:=\qHyperrphis{3}{2}@@{q^{-n},\alpha\beta q^{n+1},q^{-x}}{\alpha q,q^{-N}}{q}{q} | |||
}</math> | }</math> | ||
== Symbols List == | == Symbols List == | ||
<span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition: | <span class="plainlinks">[http://drmf.wmflabs.org/wiki/Definition:qHahn <math>{\displaystyle Q_{n}}</math>]</span> : <math>{\displaystyle q}</math>-Hahn polynomial : [http://drmf.wmflabs.org/wiki/Definition:qHahn http://drmf.wmflabs.org/wiki/Definition:qHahn]<br /> | ||
<span class="plainlinks">[http:// | <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 /><div id="drmf_foot"> | <br /><div id="drmf_foot"> | ||
<div id="alignleft"> << [[Definition: | <div id="alignleft"> << [[Definition:normctsqHahnptilde|Definition:normctsqHahnptilde]] </div> | ||
<div id="aligncenter"> [[Main_Page|Main Page]] </div> | <div id="aligncenter"> [[Main_Page|Main Page]] </div> | ||
<div id="alignright"> [[Definition: | <div id="alignright"> [[Definition:AlSalamChihara|Definition:AlSalamChihara]] >> </div> | ||
</div> | </div> |
Revision as of 04:04, 14 July 2017
The LaTeX DLMF and DRMF macro \qHahn represents the Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q} -Hahn polynomial.
This macro is in the category of polynomials.
In math mode, this macro can be called in the following ways:
- \qHahn{n}@{q^{-x}}{\alpha}{\beta}{N} produces Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \qHahn{n}@{q^{-x}}{\alpha}{\beta}{N}}}
- \qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N} produces Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N}}}
These are defined by [1]
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qHahn{N}@{q^{-x}}{\alpha}{\beta}{N}{q}=\sum_{k=0}^N \frac{\qPochhammer{\alpha\beta q^{N+1}}{q}{k}\qPochhammer{q^{-x}}{q}{k}}{\qPochhammer{\alpha q}{q}{k}\qPochhammer{q}{q}{k}}q^k }
or [2]
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \qHahn{n}@{q^{-x}}{\alpha}{\beta}{N}{q}:=\qHyperrphis{3}{2}@@{q^{-n},\alpha\beta q^{n+1},q^{-x}}{\alpha q,q^{-N}}{q}{q} }}
Symbols List
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle Q_{n}}}
: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:qHahn
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle {{}_{r}\phi_{s}}}}
: basic hypergeometric (or Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-hypergeometric) function : http://dlmf.nist.gov/17.4#E1