A generalization of the Sears--Slater transformation and elliptic Lagrange interpolation of type $BC_n$
A generalization of the Sears--Slater transformation and elliptic Lagrange interpolation of type $BC_n$
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Sears--Slater 变换和 $BC_n$ 类型的椭圆拉格朗日插值的推广
DOI：
10.1016/j.aim.2016.05.016
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
M. Noumi
中科院分区：
文献类型：
--
作者：
M. Ito;M. Noumi
以双边重基超几何级数的Sears Slater型展开式的形式，得到了B Cn型杰克逊积分的联系公式，该级数是若干特定双边重基超几何级数的线性组合.该展开式的系数由某些椭圆拉格朗日插值函数表示。通过分析椭圆型拉格朗日插值函数的基本性质，给出了相应的q-差分方程组的基本解矩阵的显式行列式公式.
The connection formula for the Jackson integral of type B C n is obtained in the form of a Sears–Slater type expansion of a bilateral multiple basic hypergeometric series as a linear combination of several specific bilateral multiple series. The coefficients of this expansion are expressed by certain elliptic Lagrange interpolation functions. Analyzing basic properties of the elliptic Lagrange interpolation functions, an explicit determinant formula is provided for a fundamental solution matrix of the associated system of q-difference equations.