Definition:discrqHermiteII

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The LaTeX DLMF and DRMF macro \discrqHermiteII represents the second discrete q π‘ž {\displaystyle{\displaystyle q}} Hermite polynomial.

This macro is in the category of polynomials.

In math mode, this macro can be called in the following ways:

\discrqHermiteII{n} produces h ~ n discrete-q-Hermite-polynomial-II-h-tilde 𝑛 {\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}
\discrqHermiteII{n}@{x}{q} produces h ~ n ⁑ ( x ; q ) discrete-q-Hermite-polynomial-II-h-tilde 𝑛 π‘₯ π‘ž {\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}\!\left(x;q\right)}}}
\discrqHermiteII{n}@@{x}{q} produces h ~ n ⁑ ( x ) discrete-q-Hermite-polynomial-II-h-tilde 𝑛 π‘₯ π‘ž {\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}\!\left(x\right)}}}

These are defined by h ~ n ⁑ ( x ; q ) := i - n ⁒ V n ( - 1 ) ⁑ ( i ⁒ x ; q ) assign discrete-q-Hermite-polynomial-II-h-tilde 𝑛 π‘₯ π‘ž superscript 𝑖 𝑛 q-Al-Salam-Carlitz-II-polynomial-V 1 𝑛 𝑖 π‘₯ π‘ž {\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}\!\left(x;q\right):=i^{% -n}V^{(-1)}_{n}\!\left(ix;q\right)}}}

Symbols List

h ~ n subscript ~ β„Ž 𝑛 {\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}  : discrete q π‘ž {\displaystyle{\displaystyle{\displaystyle q}}} -Hermite II polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteII
V Ξ± ( n ) subscript superscript 𝑉 𝑛 𝛼 {\displaystyle{\displaystyle{\displaystyle V^{(n)}_{\alpha}}}}  : Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzII


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