A Catalan constant inspired integral odyssey

@article{Stewart2020ACC,
  title={A Catalan constant inspired integral odyssey},
  author={S. Stewart},
  journal={The Mathematical Gazette},
  year={2020},
  volume={104},
  pages={449 - 459}
}
  • S. Stewart
  • Published 2020
  • Philosophy
  • The Mathematical Gazette
There is a rich and seemingly endless source of definite integrals that can be equated to or expressed in terms of Catalan's constant. Denoted by G and defined by $${\rm{G}} = \sum\limits_{n = 0}^\infty {{{{{\left( { - 1} \right)}^n}} \over {{{\left( {2n + 1} \right)}^2}}} = 1 - {1 \over {{3^2}}} + {1 \over {{5^2}}} \ldots = 0.915\,965\,594 \ldots \,\,,} $$ Scott in [1] quipped that this constant seemed almost as useful as the more widely known Euler–Mascheroni constant γ, particularly in the… Expand

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