1. G. H. Hardy andJ. E. Littlewood,The Relations between Borel’s and Cesàro’sMethods of Summation [Proceedings of the London Mathematical Society, series II, vol. XI (1912-1913), pp. 1–16].
2. For an explanation of our reasons for giving this name to the theorem, seeG. H. Hardy andJ. E. Littlewood,Contributions to the arithmetic Theory of Series [Proceedings of the London Mathematical Society, series II, vol. XI (1912–1913), pp. 411–478 (p. 413)].
3. SeeG. H. Hardy andM. Riesz,The general Theory of Dirichlet’s Series [Cambridge Mathematical Tracts, no. 18, 1915], p. 56.
4. We cannot quote any general theorem of which this equation is a direct corollary: but the materials necessary for the proof will be found in our paper « Contributions, etc. », loc. cit.2), pp. 452 et seq.
5. G. H. Hardy,The Application to Dirichlet’sSeries of Borel’sexponential Method of Summation [Proceedings of the London Mathematical Society, series 11, vol. VIII (1910), pp. 277–294].