title: Little q-Jacobi polynomials
text: # Little q-Jacobi polynomials
  
  In mathematics, the little q-Jacobi polynomials $p_n(x;a,b;q)$ are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Hahn (1949). Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.
  
  ## Definition
  
  The little q-Jacobi polynomials are given in terms of basic hypergeometric functions by
  
      $\displaystyle p_{n}(x;a,b;q)=_{2}\phi _{1}(q^{-n},abq^{n+1};aq;q,xq)$
  
  ## Gallery
  
  The following are a set of animation plots for Little q-Jacobi polynomials, with varying q; three density plots of imaginary, real and modulus in complex space; three set of complex 3D plots of imaginary, real and modulus of the said polynomials.
  
  | LITTLE q-JACOBI POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT | LITTLE q-JACOBI POLYNOMIALS IM COMPLEX 3D MAPLE PLOT | LITTLE q-JACOBI POLYNOMIALS RE COMPLEX 3D MAPLE PLOT |
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  | LITTLE q-JACOBI POLYNOMIALS ABS DENSITY MAPLE PLOT | LITTLE q-JACOBI POLYNOMIALS IM DENSITY MAPLE PLOT | LITTLE q-JACOBI POLYNOMIALS RE DENSITY MAPLE PLOT |
  