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11-11-2020
Mathematics

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Is there a general rule to convert a function to a power series? Examples would be greatly appreciated:)

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MathPhys MathPhys

11-11-2020

Step-by-step explanation:

Use the Maclaurin expansion:

f(x) = ∑ₙ₌₀°° f⁽ⁿ⁾(0) xⁿ / n!

For example, for f(x) = eˣ:

f(x) = ∑ₙ₌₀°° e⁰ xⁿ / n!

f(x) = ∑ₙ₌₀°° xⁿ / n!

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