Formula:KLS:14.05:26

From DRMF
Jump to navigation Jump to search


lim q → 1 ⁡ P n ⁡ ( x ; q α , q β , 0 ; q ) = P n ( α , β ) ⁡ ( 2 ⁢ x - 1 ) P n ( α , β ) ⁡ ( 1 ) subscript → 𝑞 1 big-q-Jacobi-polynomial-P 𝑛 𝑥 superscript 𝑞 𝛼 superscript 𝑞 𝛽 0 𝑞 Jacobi-polynomial-P 𝛼 𝛽 𝑛 2 𝑥 1 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 {\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}P_{n}\!\left(x;% q^{\alpha},q^{\beta},0;q\right)=\frac{P^{(\alpha,\beta)}_{n}\left(2x-1\right)}% {P^{(\alpha,\beta)}_{n}\left(1\right)}}}}

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

P n subscript 𝑃 𝑛 {\displaystyle{\displaystyle{\displaystyle P_{n}}}}  : big q 𝑞 {\displaystyle{\displaystyle{\displaystyle q}}} -Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqJacobi
P n ( α , β ) subscript superscript 𝑃 𝛼 𝛽 𝑛 {\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}  : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3

Bibliography

Equation in Section 14.5 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:14.05:26&oldid=4423"