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Orthogonality and Irrationality

Borwein, Peter and Dykshoorn, Willem and Erdelyi, Tamas and Zhang, John (1994) Orthogonality and Irrationality. [Preprint]

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      Abstract

      The fairly recent proofs of the irrationality of $\log 2, \pi^2, \zeta(3)$ and various values of polylogarithms are re-examined by using a particular family of orthogonal forms. This allows us to give a uniform and arguably more natural treatment of these results.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: Riemann zeta function, polylogarithm, irrationality, orthogonality, Pade approximation, Muntz-Legendre polynomial
      Subjects: 11-xx Number theory > 11Jxx Diophantine approximation, transcendental number theory
      41-xx Approximations and expansions > 41Axx Approximations and expansions
      42-xx Fourier analysis > 42Cxx Nontrigonometric Fourier series
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 16 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/74

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