Definition:qHahn: Difference between revisions

Latest revision as of 08:50, 22 December 2019

The LaTeX DLMF and DRMF macro \qHahn represents the ${\displaystyle{\displaystyle q}}$ -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

{\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(q^{-x};\alpha,\beta,N;% \right)}}}

\qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N} produces

{\displaystyle{\displaystyle{\displaystyle}{Q_{n}\!\left(q^{-x}\right)}}}

These are defined by ^[1]

{\displaystyle Q_{N}\!\left(q^{-x};\alpha,\beta,N;q\right)=\sum_{k=0}^{N}\frac% {\left(\alpha\beta q^{N+1};q\right)_{k}\left(q^{-x};q\right)_{k}}{\left(\alpha q% ;q\right)_{k}\left(q;q\right)_{k}}q^{k}}

or ^[2]

@@ Line 14: / Line 14: @@
 :'''\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 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}