【摘 要】
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In this talk,we study polynomials orthogonal with respect to a t-deformation of the q-Laguerre weight.This reduces the singularly deformed Laguerre weight when
【机 构】
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DepartmentofMathematics,UniversityofMacau
【出 处】
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International Conference on Orthogonal Polynomials,Integrabl
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In this talk,we study polynomials orthogonal with respect to a t-deformation of the q-Laguerre weight.This reduces the singularly deformed Laguerre weight when q → 1-,a weight studied by Chen and Its,and when t → 0,we recover the stand q-Laguerre weight.In the situation where 0 ＜ q ＜ 1 and t ＞ 0,a pair of q-Ladder operators,with recurrence relations,produces two subsidiary conditions,found by Chen and Ismail.Recently,Chen and Griffin,obtained the q-version of the sumrule,which laid hidden for sometime.The sum-rule reduces to that found by Magnus when q → 1-.With the sum rule we deduce,and show that quantities related to the recurrence coefficients denotes as xn and yn satisfy a pair non-linear difference equations,which are akin to the recognized asymmetric discrete Painleve systems such as α q-P-IV and q-P-V.We also give a quick review on the asymptotic behavior of a doubly scaled Hankel determinant-the q → 1-case obtained a number of years ago by Chen and Its(Ⅱ).
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