Formula:KLS:14.06:23

From DRMF
Jump to navigation Jump to search


R n ⁡ ( μ ⁢ ( x ) ; α , β , 0 , β - 1 ⁢ q - N - 1 | q ) = Q n ⁡ ( q - x ; α , β , N ; q ) q-Racah-polynomial-R 𝑛 𝜇 𝑥 𝛼 𝛽 0 superscript 𝛽 1 superscript 𝑞 𝑁 1 𝑞 q-Hahn-polynomial-Q 𝑛 superscript 𝑞 𝑥 𝛼 𝛽 𝑁 𝑞 {\displaystyle{\displaystyle{\displaystyle R_{n}\!\left(\mu(x);\alpha,\beta,0,% \beta^{-1}q^{-N-1}\,|\,q\right)=Q_{n}\!\left(q^{-x};\alpha,\beta,N;q\right)}}}

Substitution(s)

μ ⁢ ( n ) = q - n + α ⁢ β ⁢ q n + 1 𝜇 𝑛 superscript 𝑞 𝑛 𝛼 𝛽 superscript 𝑞 𝑛 1 {\displaystyle{\displaystyle{\displaystyle\mu(n)=q^{-n}+\alpha\beta q^{n+1}}}} &
μ ⁢ ( x ) = q - x + γ ⁢ δ ⁢ q x + 1 𝜇 𝑥 superscript 𝑞 𝑥 𝛾 𝛿 superscript 𝑞 𝑥 1 {\displaystyle{\displaystyle{\displaystyle\mu(x)=q^{-x}+\gamma\delta q^{x+1}}}}


Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

& : logical and
R n subscript 𝑅 𝑛 {\displaystyle{\displaystyle{\displaystyle R_{n}}}}  : q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -Racah polynomial : http://dlmf.nist.gov/18.28#E19
Q n subscript 𝑄 𝑛 {\displaystyle{\displaystyle{\displaystyle Q_{n}}}}  : q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:qHahn

Bibliography

Equation in Section 14.6 of KLS.

URL links

We ask users to provide relevant URL links in this space.


Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Formula:KLS:14.06:23&oldid=4551"