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In this paper we consider the orthogonal polynomials with weights $w_\alpha(x)= x^\alpha \exp(-x^3+tx)$ and $W_\alpha(x)=|x|^{2\alpha+1} \exp(-x^6+tx^2)$. Using the compatibility conditions for the ladder operators for these orthogonal polynomials, we derive several difference equations satisfied by the recurrence coefficients of these orthogonal polynomials. We also derive differential-difference equations and second order linear ordinary differential equations satisfied by these orthogonal polynomials.
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참고문헌 (6)
참고문헌 신청
Boelen L / 2011 / Recurrence coe cients of generalized Meixner polynomials and Painlev e equations / J. Phys. A: Math. Theor 44:35202
Bonan S / 1986 / Estimates of the orthogonal polynomials with weight exp( xm), m an even positive integer / J. Approx. Theory 46:408~410
Chen Y / 2005 / Jacobi polynomials from compatibility conditions / Proc. Am. Math. Soc 133:465~472
Chihara T S / 1978 / An introduction to orthogonal polynomials / Gordon and Breach
Filipuk G / 2012 / The recurrence coe cients of semi-classical Laguerre polynomials and the fourth Painlev e equation / J. Phys. A : Math. Theor 45:205201
Bonan S / 1986 / Estimates of the orthogonal polynomials with weight exp( xm), m an even positive integer / J. Approx. Theory 46:408~410
Chen Y / 2005 / Jacobi polynomials from compatibility conditions / Proc. Am. Math. Soc 133:465~472
Chihara T S / 1978 / An introduction to orthogonal polynomials / Gordon and Breach
Filipuk G / 2012 / The recurrence coe cients of semi-classical Laguerre polynomials and the fourth Painlev e equation / J. Phys. A : Math. Theor 45:205201
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