Abstract: This paper develops a method of expansions for complex functions in the neighborhood of its branchpoint. Its expansion turns into the form of integral when it comes to infinite-order branch points, which is named after Laurent transform. Attempt is employed to try to get the expansion of several sample functions, with judging the completeness for the expansions. Plus, to use the form of complex-power expansions instead of real-power ones is imagined. One example is employed in signal system to explain its practical application and future prospect at last.

Key words: complex varied functions, Laurent integral, basis, signal system