A Set of 4 { Quad-Symmetric Based } Functions

by Frank C. Fung - 1st published in March, 2008.

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Summary of Findings

Key Findings :

• We simply set-up 4 { Q-Functions } defined by :
  • 

    

    

    

    so that :

  • 

    

    

    

  And these 4 { Q-Functions } are { quad-symmetric based } to the extent that :

  • the { derivative relations } are circular in nature , so that :
    • any one of the 4 functions may be chosen the { lead-off } function for an analysis ,

      and the result would be quite similar .

  We can then express :

  • 

    and

  • 

    

    If we take [ sigma ] as purely { real } and [ x ] as purely { imaginary } ,

    • these 2 equations could possibly contribute to a finer understanding of the { sine } and { cosine } functions on the { complex plane } .

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go to the next section : Section I - The Search for { Quad-Symmetric Based } Functions

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Original dated 2008-3-23 *** Updated 2008-11-01 / 2009-10-26