Question

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

Answer 1

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!