Biorthogonal Expansion of Non-Symmetric Jack Functions⋆
نویسنده
چکیده
We find a biorthogonal expansion of the Cayley transform of the non-symmetric Jack functions in terms of the non-symmetric Jack polynomials, the coefficients being Meixner–Pollaczek type polynomials. This is done by computing the Cherednik–Opdam transform of the non-symmetric Jack polynomials multiplied by the exponential function.
منابع مشابه
Biorthogonal polynomials and numerical quadrature formulas for some finite-range integrals with symmetric weight functions
MSC: 41A55 41A60 65B05 65B10 65B15 65D30 Keywords: Biorthogonal polynomials Numerical integration Symmetric weight functions Acceleration of convergence Levin transformation Rational approximation a b s t r a c t In this work, we derive a family of symmetric numerical quadrature formulas for finite-range integrals I[f ] = 1 −1 w(x)f (x) dx, where w(x) is a symmetric weight function. In partic...
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