Augustin Louis Cauchy

Augustin Louis Cauchy was a French mathematician born in 1789, died in 1857.

• He developed a test for convergence? of an infinite series of numbers.
  • this test is that given a sequence p_n,
    • the series (sumover) p<sub>n</n> and (sumover) 2<super>n</super>p_{2<super>n</super>} either both diverge or both converge.
  • this is applicable to [improper integrals]?, families of functions, and series by verifying that a Cauchy sequence is obtained, and then using the underlying metric space's completeness to show convergence.