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Main SMS (2006)

December 23, 2006


  The formula below is true for all .

Click here to see more formulas and examples.

December 13, 2006


 The reciprocal of the beautiful infinite product of nested radicals

due to Vieta in 1592 can be decomposed into partial fractions of the infinite series as shown below or click here.


October 15, 2006


Finite Alternative Odd Power Series
The sums of the following identities are true for any positive integer n.




  •    .



More >>


September 17, 2006



August 25, 2006
GraphFunc is an online program for drawing graphs of basic mathematical functions in 2D and 3D coordinate systems.  Click here to use this tool.
(August 1, 2006)


  • The new fast convergent series is found for computing the constant log 2.

July 04, 2006

(Twin series – when comparing this series and the one shown below)

May 29, 2006


A fast convergent series of BPP-type formulas has been found and can be used for computing the n-th digit of in base 4096 without computing any prior digits. 

  •  .
(We do not know whether this series is new)

May 28, 2006

  • .

(This series has been found and can be used to compute directly the n-th digit of ln(7) without computing any prior digits. Notice that the base of this series is 729.)


May 23, 2006


May 15, 2006





April 21, 2006



March 7, 2006

  • or it can be written in product form:
  •  .

March 6, 2006

  •  .


This series can be written in product form:

, which is


March 4, 2006



January 16, 2006


  •  (new?)
  • (new?)
  • (new?)
  • (a beautiful series.  This series can be found in Ramanujan’s second notebook)




Note: the author, who created and posted these series on this page, sent 'the idea of these series' to a 'guy' who published the new findings based on Ramanujan's original series for requesting whether those series above are new.  There were no answers but ... four months later that 'guy' published in his another article and indicated that the findings in his earlier publish was in the bad direction, and he recomputed his findings based on 'the idea of these series' without mentioning the source of the original inspiration leading to that change!

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I am interested in mathematics only as a creative art.  
 Godfrey Harold Hardy