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by Ciro Santilli (@cirosantilli, 37)

Taylor expansion definition of the exponential function

 ... Function (mathematics) Function by signature Numeric function Exponentiation Exponential function Definition of the exponential function
 0 By others on same topic  0 Discussions  Updated 2025-05-29  +Created 1970-01-01  See my version
The Taylor series expansion is the most direct definition of the expontial as it obviously satisfies the exponential function differential equation:
  • the first constant term dies
  • each other term gets converted to the one before
  • because we have infinite many terms, we get what we started with!
ex=∑n=0∞​n!xn​=1+1x​+2x2​+2×3x3​+2×3×4x4​+…
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  1. Definition of the exponential function
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  • Exponential map (Lie theory)

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