The generalized Krawtchouk polynomials and the fifth Painlev\'e equation
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🧮 math.CA
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coefficientsequationfifthkrawtchoukpainlevpolynomialsweightcoupled
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We study the recurrence coefficients of the orthogonal polynomials with respect to a semi-classical extension of the Krawtchouk weight. We derive a coupled discrete system for these coefficients and show that they satisfy the fifth Painlev\'e equation when viewed as functions of one of the parameters in the weight.
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