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)ⁿ F(s) is represented in that domain by the power series ...
By collecting the terms that make up the coefficient of (s-s0)ⁿֿ¹ 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.
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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.