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Taylor expansion definition of the exponential function

Ciro Santilli (@cirosantilli, 37) ... Function (mathematics) Function by signature Numeric function Exponentiation Exponential function Definition of the exponential function
Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own 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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