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A Maclaurin series is a special case of a Taylor series where the center of expansion is exactly 0. A Taylor series generalizes this by allowing the expansion to be centered at an arbitrary point a.

Conditions: The Taylor formula is taken with center a.; Setting $a=0$ recovers the displayed Maclaurin formula.

A Maclaurin series is a special case of a Taylor series where the center of expansion is exactly 0. A Taylor series generalizes this by allowing the expansion to be centered at an arbitrary point a.

Conditions: The Taylor formula is taken with center a.; Setting $a=0$ recovers the displayed Maclaurin formula.