To protect client privacy in federated learning, Differential Privacy (DP) techniques are widely adopted, but the integration of DP introduces additional heterogeneity among clients, negatively impacting model accuracy. To address the heterogeneity caused by DP, the state-of-the-art method uses linear transformations to adjust data distributions, this reduces the heterogeneity introduced by DP. However, the noise scales proportionally with the linear transformations. For example, certain edge features mixed with noise may be amplified beyond acceptable boundaries, leading to suboptimal results and the loss of critical edge features, thereby limiting improvements in model accuracy. To overcome these challenges, this paper proposes a polynomial transformation method based on generating functions. The method combines nonlinear and linear transformations to adjust client distributions more effectively. By applying polynomial transformations to the original data, it refines the data distribution and captures complex patterns and edge features. As a result, the method reduces client heterogeneity and improves model accuracy. Experimental results demonstrate that the proposed method significantly enhances model accuracy and reduces client heterogeneity across various datasets and privacy budgets.