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I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ...

I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ...

I need help with some aspects of Examples 1.1 and 1.2, Section 1.2, Chapter III ...

Examples 1.1 and 1.2, Section 1.2, Chapter III read as follows:

View attachment 9334

My questions regarding the above two examples from Palka are as follows:

Can someone please explain where in the calculations of Example 1.1 does the assumption of n being positive becomes relevant ...

I am puzzled because it appears that each of the steps of the calculation are true whether n is positive or negative ...

Can someone please explain where in the calculations of Example 1.2 does the assumption of n being negative becomes relevant ...

I am puzzled because it appears that each of the steps of the argument/calculation are true whether n is positive or negative ...Hope someone can help ...

Help will be much appreciated ...

Peter

I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ...

I need help with some aspects of Examples 1.1 and 1.2, Section 1.2, Chapter III ...

Examples 1.1 and 1.2, Section 1.2, Chapter III read as follows:

View attachment 9334

My questions regarding the above two examples from Palka are as follows:

*Question 1*Can someone please explain where in the calculations of Example 1.1 does the assumption of n being positive becomes relevant ...

I am puzzled because it appears that each of the steps of the calculation are true whether n is positive or negative ...

*Question 2*

Can someone please explain where in the calculations of Example 1.2 does the assumption of n being negative becomes relevant ...

I am puzzled because it appears that each of the steps of the argument/calculation are true whether n is positive or negative ...Hope someone can help ...

Help will be much appreciated ...

Peter