= Big q-Legendre polynomials
{wiki=Big_q-Legendre_polynomials}
The Big \\( q \\)-Legendre polynomials are a generalization of the classical Legendre polynomials, which arise in various areas of mathematics, including orthogonal polynomial theory and special functions. The \\( q \\)-analog of mathematical concepts replaces conventional operations with ones that are compatible with the \\( q \\)-calculus, often leading to new insights and applications, particularly in combinatorial contexts, statistical mechanics, and quantum algebra.
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