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11 results

  • On 107.27

  • Graham Jameson
  • Journal:
    The Mathematical Gazette / Volume 107 / Issue 570 / November 2023
    Published online by Cambridge University Press:
    11 October 2023, p. 549
    Print publication:
    November 2023
    • Article
      • You have access
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  • Correspondence

  • Graham Jameson, Pauline Jameson
  • Journal:
    The Mathematical Gazette / Volume 102 / Issue 553 / March 2018
    Published online by Cambridge University Press:
    08 February 2018, p. 171
    Print publication:
    March 2018
    • Article
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  • Integrals evaluated in terms of Catalan's constant

  • Graham Jameson, Nick Lord
  • Journal:
    The Mathematical Gazette / Volume 101 / Issue 550 / March 2017
    Published online by Cambridge University Press:
    03 February 2017, pp. 38-49
    Print publication:
    March 2017

  • Catalan's constant, named after E. C. Catalan (1814-1894) and usually denoted by G, is defined by

    It is, of course, a close relative of

    The numerical value is G ≈ 0.9159656. It is not known whether G is irrational: this remains a stubbornly unsolved problem. The best hope for a solution might appear to be the method of Beukers [1] to prove the irrationality of ζ (2) directly from the series, but it is not clear how to adapt this method to G.

  • Some remarkable integrals derived from a simple algebraic identity

  • Graham J. O. Jameson, Timothy P. Jameson
  • Journal:
    The Mathematical Gazette / Volume 97 / Issue 539 / July 2013
    Published online by Cambridge University Press:
    23 January 2015, pp. 205-209
    Print publication:
    July 2013

  • The identity in question really is simple: it says, for u ≠ −1,

    We describe two types of definite integral that look quite formidable, but dissolve into a much simpler form by an application of (1) in a way that seems almost magical.

    Both types, or at least special cases of them, have been mathematical folklore for a long time. For example, case (10) below appears in [1, p. 262], published in 1922 (we are grateful to Donald Kershaw for showing us this example). However, they do not seem to figure in most books on calculus except possibly tucked away as an exercise The comprehensive survey [2] mentions the second type on p. 253, but only as a lemma on the way to an identity the authors call the ‘master formula’ We come back to this formula later, but only after describing a number of other more immediate applications.