Definition:discrqHermiteI

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The LaTeX DLMF and DRMF macro \discrqHermiteI represents the first 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:

\discrqHermiteI{n} produces h n discrete-q-Hermite-polynomial-h-I 𝑛 {\displaystyle{\displaystyle{\displaystyle h_{n}}}}
\discrqHermiteI{n}@{x}{q} produces h n ⁑ ( x ; q ) discrete-q-Hermite-polynomial-h-I 𝑛 π‘₯ π‘ž {\displaystyle{\displaystyle{\displaystyle h_{n}\!\left(x;q\right)}}}
\discrqHermiteI{n}@@{x}{q} produces h n ⁑ ( x ) discrete-q-Hermite-polynomial-h-I 𝑛 π‘₯ π‘ž {\displaystyle{\displaystyle{\displaystyle h_{n}\!\left(x\right)}}}

These are defined by h n ⁑ ( x ; q ) := U n ( - 1 ) ⁑ ( x ; q ) assign discrete-q-Hermite-polynomial-h-I 𝑛 π‘₯ π‘ž q-Al-Salam-Carlitz-I-polynomial-U 1 𝑛 π‘₯ π‘ž {\displaystyle{\displaystyle{\displaystyle h_{n}\!\left(x;q\right):=U^{(-1)}_{% n}\!\left(x;q\right)}}}

Symbols List

h n subscript β„Ž 𝑛 {\displaystyle{\displaystyle{\displaystyle h_{n}}}}  : discrete q π‘ž {\displaystyle{\displaystyle{\displaystyle q}}} -Hermite I polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteI
U Ξ± ( n ) subscript superscript π‘ˆ 𝑛 𝛼 {\displaystyle{\displaystyle{\displaystyle U^{(n)}_{\alpha}}}}  : Al-Salam-Carlitz I polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzI


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