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An Alternating Product Representation for Real Numbers

In: Applications of Fibonacci Numbers

Author

Listed:
  • Arnold Knopfmacher
  • John Knopfmacher

Abstract

In 1770 Lambert introduced two positive series expansions for the real numbers in terms of rationals. These were subsequently rediscovered by Sylvester (1880) and Engel (1913) after whom they are respectively named. A further positive series expansion for the real numbers was discovered by Lüroth (1883). Also of particular interest to us is the product expansion of Cantor (1869). More recently, Oppenheim [3] defined a general algorithm for expressing real numbers in terms of a positive series of rational numbers. All of the previously mentioned expansions were shown to be special cases of the Oppenheim algorithm.

Suggested Citation

  • Arnold Knopfmacher & John Knopfmacher, 1990. "An Alternating Product Representation for Real Numbers," Springer Books, in: G. E. Bergum & A. N. Philippou & A. F. Horadam (ed.), Applications of Fibonacci Numbers, pages 209-216, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-1910-5_24
    DOI: 10.1007/978-94-009-1910-5_24
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