Formula:KLS:14.05:80

<< Formula:KLS:14.05:79

formula in Big q-Jacobi: Special case

Formula:KLS:14.05:81 >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}P_{n}\!\left(x;0;q\right)=\LegendrePoly{n}@{2x-1}}}}$

Proof

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Symbols List

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

Bibliography

Equation in Section 14.5 of KLS.

URL links

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<< Formula:KLS:14.05:79

formula in Big q-Jacobi: Special case

Formula:KLS:14.05:81 >>