本文在传统的留数计算方法的基础上，提出了三种改进的留数计算方法，并给出了应用实例。

This paper presents three improved methods on calculation of residues based on the traditional methods, and gives the applied example for these methods.

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本文在传统的留数计算方法的基础上，提出了三种改进的留数计算方法，并给出了应用实例。

The present paper presents three improved methods on calculation of residues based on the traditional methods, and gives the applied example for these methods.

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推广了留数理论中的对数留数定理，给出了一般性的结论，从而解决了一类函数的留数计算问题。

The traditional logarithmic residue theorem is generalized, so a general conclusion is given to solve the calculating for residue.

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