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Lejeune Dirichlet, P.G. (1829) Sur la convergence des séries trigonométriques qui servent à répresenter une fonction arbitraire entre des limites donées. Journal für reine and angewandte Mathematik, 4, 157-169.

has been cited by the following article:

• TITLE: Pringsheim Convergence and the Dirichlet Function

  AUTHORS: Thomas Beatty, Bradley Hansen

  KEYWORDS: Convergence, Pointwise Limit, Double Sequence, Pringsheim, Dirichlet Function, Baire Category Theorem, Cosine

  JOURNAL NAME: Advances in Pure Mathematics, Vol.6 No.6, May 24, 2016

  ABSTRACT: Double sequences have some unexpected properties which derive from the possibility of commuting limit operations. For example, may be defined so that the iterated limits and exist and are equal for all x, and yet the Pringsheim limit does not exist. The sequence is a classic example used to show that the iterated limit of a double sequence of continuous functions may exist, but result in an everywhere discontinuous limit. We explore whether the limit of this sequence in the Pringsheim sense equals the iterated result and derive an interesting property of cosines as a byproduct.