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Mehler-Heine formulas for orthogonal polynomials with respect to the modified Jacobi weight. (English) Zbl 1290.42054
Summary: The ladder operator approach has been applied to deduce the Mehler-Heine type formulas for orthogonal polynomials with respect to the modified Jacobi weight \[ \omega_{\alpha\beta ,h}(x)=h(x)(1-x)^\alpha(1+x)^\beta, \quad x\in [-1,1], \] where \(\alpha\), \(\beta > 0\), and with \(h\) real analytic and strictly positive on \([-1,1]\).

MSC:
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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