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New formulae for higher order derivatives and a new algorithm for numerical integration

  • Author / Creator
    Slevinsky, Richard
  • This thesis is concerned with the development of new formulae for higher order derivatives, and the algorithmic, numerical, and analytical development of the G transformation, a method for computing infinite-range integrals. We introduce the Slevinsky-Safouhi formulae I and II with applications, we develop an algorithm for the G transformation, we derive explicit approximations to incomplete Bessel functions and tail probabilities of five probability distributions from the recursive algorithm for the G transformation, and we present all extant work on the analysis of the convergence properties of the G transformation.

  • Subjects / Keywords
  • Graduation date
    2011-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R36H0W
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Supervisor / co-supervisor and their department(s)
    • Safouhi, Hassan (Campus Saint-Jean and Adjunct Mathematical and Statistical Sciences)
    • Lau, Anthony (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Lau, Anthony (Mathematical and Statistical Sciences)
    • Penin, Alexander (Physics)
    • Safouhi, Hassan (Campus Saint-Jean and Adjunct Mathematical and Statistical Sciences)
    • Dai, Feng (Mathematical and Statistical Sciences)