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Main SMS (2008)

We work on exploring and developing math series.  Each time a series or a group of series has been developed completely, it is posted on this website.  Below are the patterns of some series listed in date order.  More related series can be found in the Series Outline Book section, which consists of Random Series and Series SummaryRandom Series is a place where it keeps all math series without classifying to a specific type.  Series Summary is a SMS's part in which it keeps the math series in relation to the dates posted on this website.

 


December 14, 2008

 
 
An infinite series has a connection with one of the roots of the quartic equation and the constant Pi.
 
,
where  
, which is one of the roots of the quartic equation
 
                     .
 

December 13, 2008
 
 
The Riemann Zeta (7) constant has been found in a series in which the hyperbolic functions and other math constants appear.
 
 
, where is a Riemann zeta constant.

  
 
August 12, 2008

 

  The infinite series of the BBP-type formula is found and used to compute the digits of the constant .

 
.
 
Another series is found in terms of other math constants, namely
 
.
 
Click here to see other similar series of this type.
 

August 2, 2008
  
 
General Inverse Tangent Series of Unknown Names
        ,
 
where , , and.
 
It reveals many inverse tangent and Machine-like formulas. For example, the simple one of this type is obtained when n = 1, namely
 
            .
 
Click here to see other forms.
 



May 1, 2008
 
 
Power Sum and Sum of Partial Power Sums for any positive integer n. 
 
Power Sum
 
      
                      
  
 
Sum of Partial Power Sums
 
                  
Click here to see other similar formulas.
   

January 31, 2008

 

 
 
.
 
  

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Divided by 0 is often where a transcendental number or an irrational number emerges.  
(T.V.)