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Original Articles

Some comprehensive expressions for π and 1/π

Pages 91-100 | Received 24 Jul 1990, Published online: 19 Mar 2007

References

  • 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 harmonic oscillator yields monotonic series for the mathematical constant π . Journal of Computational and Applied Mathematics , 30 : 127 – 137 .
  • Merzbacher , E. 1970 . Quantum Mechanics , 2nd Ed , 71 – 71 . New York : Wiley .
  • 209 Op. cit.
  • Eves , H. 1954 . An Introduction to the History of Mathematics , 93 – 93 . New York : Holt, Rinehart, and Winston .
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  • Sneddon , I. N. 1980 . Special Functions of Mathematical Physics and Chemistry , 3rd Ed. , 37 – 37 . London : Longman .
  • Gradshteyn I. S. Ryzhik I. M. Op. cit. 11
  • Erdélyi , A. 1953 . Higher Transcendental Functions , Vol. 1 , 47 – 47 . New York : McGraw-Hill .
  • Borwein , J. M. and Borwein , P. B. 1984 . The arithmetic-geometric mean and fast computation of elementary functions . SIAM Review , 26 : 351 – 366 .
  • Borwein , J. M. , Borwein , P. B. , Bailey , D. H. and Ramanujain . 1989 . Modular equations, and approximations to pi or how to compute one billion digits of pi . American Mathematical Monthly , 96 ( 3 ) : 201 – 219 .

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