Formula:KLS:14.12:42

<< Formula:KLS:14.12:41

formula in Little q-Jacobi: Special case

Formula:KLS:14.13:01 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}p_{n}\!\left(x|q\right)=\LegendrePoly{n}@{1-2x}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLegendre
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : Legendre polynomial : http://dlmf.nist.gov/18.3#T1.t1.r25

Bibliography

Equation in Section 14.12 of KLS.

URL links

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<< Formula:KLS:14.12:41

formula in Little q-Jacobi: Special case

Formula:KLS:14.13:01 >>