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Original Articles

The wallis formula for PI, including two new expressions involving irrationals

Pages 197-203 | Received 10 May 1991, Published online: 19 Mar 2007

References

  • Castellanos , D. 1988 . The Ubiquitous π . Mathematics Magazine , 61 : 67 – 98 .
  • Castellanos D. The Ubiquitous π Mathematics Magazine 1988 61 148 163 M. Kline, Mathematics Magazine 56 (1983), 307-314.
  • Borwein , J. M. , Borwein , P. B. , Bailey , D. H. and Ramanujan . 1989 . Modular Equations, and Approximations to P1 or How to Compute One Billion Digits for P1 . American Mathematical Monthly , 96 : 201 – 219 .
  • Eves , H. 1954 . An Introduction to the History of Mathematics , 93 – 93 . New York : Holt, Rinehart and Winston .
  • Beckmann P. A History of Pi Springer-Verlag Golem, Boulder 1977 572 125 Isaac Newton discovered the calculus 10 years after Wallis derived this famous result in his Arithmetica Infinitorum. Thus in order to evaluate the area of a quadrant of the unit circle ∫1- Wallis used interpolations and inductive procedures
  • Op. cit. p. 128
  • Gradshteyn , I.S. and Ryzhik , I. M. 1980 . Tables of Integrals, Series and Products , 294 – 294 . New York : Academic Press . prepared by A.Jeffrey
  • Mavromatis , H. A. 1990 . Two Doubly Infinite Sets of Series for π . Journal of Approximation Theory , 60 : 1 – 10 .
  • Lynch , R. and Mavromatis , H. A. 1990 . N-dimensional harmonics oscillator yields monotonic series for the mathematical constant π . Journal of Computational and Applied Mathematics , 30 : 127 – 137 .
  • Mavromatis , H. A. 1991 . Some Comprehensive Expressions for π and 1/π . International Journal of Computer Mathematics , 38 : 91 – 100 .

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