Definition:qBesselPoly: Difference between revisions

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Latest revision as of 08:49, 22 December 2019

The LaTeX DLMF and DRMF macro \qBesselPoly represents the q 𝑞 {\displaystyle{\displaystyle q}} -Bessel polynomial.

This macro is in the category of polynomials.

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

\qBesselPoly{n} produces y n q-Bessel-polynomial-y 𝑛 {\displaystyle{\displaystyle{\displaystyle y_{n}}}}
\qBesselPoly{n}@{x}{b}{q} produces y n ( x ; b ; q ) q-Bessel-polynomial-y 𝑛 𝑥 𝑏 𝑞 {\displaystyle{\displaystyle{\displaystyle y_{n}\!\left(x;b;q\right)}}}

These are defined by y n ( x ; a ; q ) := \qHyperrphis 21 @ @ q - n , - a q n 0 q q x assign q-Bessel-polynomial-y 𝑛 𝑥 𝑎 𝑞 \qHyperrphis 21 @ @ superscript 𝑞 𝑛 𝑎 superscript 𝑞 𝑛 0 𝑞 𝑞 𝑥 {\displaystyle{\displaystyle{\displaystyle y_{n}\!\left(x;a;q\right):=% \qHyperrphis{2}{1}@@{q^{-n},-aq^{n}}{0}{q}{qx}}}\)\@add@PDF@RDFa@triples\end{document}}

Symbols List

y n subscript 𝑦 𝑛 {\displaystyle{\displaystyle{\displaystyle y_{n}}}}  : q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -Bessel polynomial : http://drmf.wmflabs.org/wiki/Definition:qBessel
ϕ s r subscript subscript italic-ϕ 𝑠 𝑟 {\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}  : basic hypergeometric (or q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -hypergeometric) function : http://dlmf.nist.gov/17.4#E1