Meixner polynomials (MNPs) and their moments are considered significant feature extraction tools because of their salient representation in signal processing and computer vision. However, the existing recurrence algorithm of MNPs exhibits numerical instabilities of coefficients for high-order polynomials. This paper proposed a new recurrence algorithm to compute the coefficients of MNPs for high-order polynomials. The proposed algorithm is based on a derived identity for MNPs that reduces the number of the utilized recurrence times and the computed number of MNPs coefficients. To minimize the numerical errors, a new form of the recurrence algorithm is presented. The proposed algorithm computes \(\sim \)50% of the MNP coefficients. A comparison with different state-of-the-art algorithms is performed to evaluate the performance of the proposed recurrence algorithm in terms of computational cost and reconstruction error. In addition, an investigation is performed to find the maximum generated size. The results show that the proposed algorithm remarkably reduces the computational cost and increases the generated size of the MNPs. The proposed algorithm shows an average improvement of \(\sim \)77% in terms of computation cost. In addition, the proposed algorithm exhibits an improvement of \(\sim \)1269% in terms of generated size.

Meixner多项式（MNP）及其矩被认为是重要的特征提取工具，因为它们在信号处理和计算机视觉中的显着表现。但是，现有的MNP递归算法在高阶多项式上表现出系数的数值不稳定性。提出了一种新的递归算法来计算高阶多项式的MNP系数。所提出的算法基于MNP的派生身份，从而减少了所利用的重复次数和计算出的MNP系数数量。为了最小化数值误差，提出了一种新形式的递归算法。所提出的算法计算\（\ sim \）MNP系数的50％。与不同的最新算法进行了比较，以从计算成本和重构误差方面评估所提出的递归算法的性能。另外，进行调查以找到最大产生的尺寸。结果表明，该算法显着降低了计算成本，并增加了MNP的生成大小。所提出的算法在计算成本方面平均提高了（\ sim \） 77％。另外，所提出的算法在生成大小方面表现出对\（\ sim \） 1269％的改进。