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exp

Represents the exponential function with base e (Euler's number), commonly used in mathematical and scientific notation.

Overview

A fundamental mathematical function essential in calculus, differential equations, and complex analysis, providing a more elegant way to express e raised to a power than using direct superscript notation.

  • Preferred over e^x notation in professional mathematical writing
  • Particularly important in differential equations and growth/decay problems
  • Frequently used in probability theory and statistics
  • Maintains better readability with complex exponents
  • Standard notation in scientific literature and academic papers

Examples

Natural exponential function with a simple variable.

f(x)=exp(x)f(x) = \exp(x)
f(x) = \exp(x)

Solution to a differential equation showing exponential decay.

y(t)=Aexp(λt)y(t) = A\exp(-\lambda t)
y(t) = A\exp(-\lambda t)

Complex exponential in Euler's formula.

exp(ix)=cosx+isinx\exp(ix) = \cos x + i\sin x
\exp(ix) = \cos x + i\sin x