I would just like some help on the theory of maths. If a question asks for proof of a function using the Taylor Series Expansion, can you use the Maclaurin Series? Is using the Maclaurin Series regarded as using the Taylor Series Expansion or not? If I'm totally on the wrong track, would someone care to explain, please?
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The Maclaurin series is a special case of the Taylor series. So certainly you can use the Maclaurin series: you will be using a Taylor series.
Many people do not even use the term Maclaurin series.