The Sophomore's Dream


Title: The Sophomore's Dream
Author: Manuel Eberl
Submission date: 2022-04-10

This article provides a brief formalisation of the two equations known as the Sophomore's Dream, first discovered by Johann Bernoulli in 1697:

\[\int_0^1 x^{-x}\,\text{d}x = \sum_{n=1}^\infty n^{-n} \quad\text{and}\quad \int_0^1 x^x\,\text{d}x = -\sum_{n=1}^\infty (-n)^{-n}\]
  author  = {Manuel Eberl},
  title   = {The Sophomore's Dream},
  journal = {Archive of Formal Proofs},
  month   = apr,
  year    = 2022,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License