Math 2.0

definition

Maclaurin series

Definition

Let II be an open interval with 0∈I0 \in I, and let f ⁣:I→Rf \colon I \to \mathbb{R} be smooth. The Maclaurin series of ff is its Taylor series at 00: ∑n=0∞f(n)(0)n!xn.\sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!} x^n.

Remarks

For example, the Maclaurin series of exe^x is ∑xn/n!\sum x^n / n!, and the one of 1/(1−x)1/(1 - x) is ∑xn\sum x^n. The series is named after Colin Maclaurin.

Explanations

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A Maclaurin series is a Taylor series centered at 00.

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Limit point of a set, definition, no evidence levelLimit point of a setdefinitionSequence, definition, no evidence levelSequencedefinitionLimit of a function, definition, no evidence levelLimit of a functiondefinitionReal sequence, definition, no evidence levelReal sequencedefinitionContinuity at a point, definition, no evidence levelContinuity at a pointdefinitionDerivative, definition, no evidence levelDerivativedefinitionSeries, definition, no evidence levelSeriesdefinitionContinuous function, definition, no evidence levelContinuous functiondefinitionDifferentiable function, definition, no evidence levelDifferentiable functi…definitionPower series, definition, no evidence levelPower seriesdefinitionDerivative function, definition, no evidence levelDerivative functiondefinitionHigher derivative, definition, no evidence levelHigher derivativedefinitionTaylor polynomial, definition, no evidence levelTaylor polynomialdefinitionContinuously differentiable function, definition, no evidence levelContinuously differen…definitionSmooth function, definition, no evidence levelSmooth functiondefinitionTaylor series, definition, no evidence levelTaylor seriesdefinitionMaclaurin series, definition, no evidence levelMaclaurin seriesdefinition
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  1. Limit point of a set definition
  2. Sequence definition
  3. Limit of a function definition
  4. Real sequence definition
  5. Continuity at a point definition
  6. Derivative definition
  7. Series definition
  8. Continuous function definition
  9. Differentiable function definition
  10. Power series definition
  11. Derivative function definition
  12. Higher derivative definition
  13. Taylor polynomial definition
  14. Continuously differentiable function definition
  15. Smooth function definition
  16. Taylor series definition
  17. Maclaurin series definition

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Sources

  1. Web https://en.wikipedia.org/wiki/Taylor_series, Definition

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