Explore BrainMass

Explore BrainMass

    Punctured Disk : Poles, Taylor Series, Laurent Series and Power Series

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Suppose that a function F(s) has a pole of order m at s=s0, with a Laurent series expansion ... in the punctured disk 0<|s - s0|<R2, and note that (s-s0)&#8319; F(s) is represented in that domain by the power series ...
    By collecting the terms that make up the coefficient of (s-s0)&#8319;­&#1471;¹ in the product (Sec. 61) of this power series and the Taylor series expansion ... of the entire function ... show that ... as stated at the beginning of Sec. 82.

    Please see attachment for full question.

    © BrainMass Inc. brainmass.com December 24, 2021, 5:14 pm ad1c9bdddf


    Solution Summary

    Poles, Taylor Series, Laurent Series and Power Series are investigated for a Punctured Disk. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.