Problem

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Let

(*)

Evaluate this formula for

using the power series expansion for f at q = 0:

(1)

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I have two questions.

1.) Is this power series expansion correct? I tried inputting this function in MATLAB and it gives me a different power series expansion:

(2)

2. Regarding the power series which is defined as

at q = a.

Since this power series (1) I do not understand how a power series can be derived this way since at q = 0, then f(0) from (*) is undefined because we can not divide by 0, correct?

Thank you for reading.