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Main SMS (2009)

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 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 20, 2009


Infinite Series in Connection with Pi Constant 




November 26, 2009 (Happy Thanksgiving)


Finite Series in Connection with Apéry, Pi Constants

The n-th partial sum below is expressed in terms of Hurwitz zeta function for each positive integer n.  



 , s and a are complex variables.  

More >>


November 07, 2009


Finite Series Are Expressed  in Terms of n-th Partial Sum of Hurwitz Zeta Function

For real x and each positive integer n, 

,   x ≠ - k, - (k+1).

This finite series is defined in the Hurwitz zeta function form. Read more >>


October 25, 2009


Finite Series in General Form

For real x ≠ 0 and each positive integer n, 


More >>


September 26, 2009


50 Identities of Power Summation (Update)


July 8, 2009


A Family of Finite BBP-Type Series in the Base of 729

 For each positive integer n,

July 1, 2009


Some BBP-Type Series for Computing Pi (Update)

  • .


  • .

More >>



June 14, 2009
A Brief Note of the Sum of Riemann Zeta Function and the Digamma Function
The sum of Riemann zeta function,, is found in the closed-form.

 More >>



April 12, 2009 and May 3, 2009


Some Finite Series Found in Closed-Form

For each positive integer n, the following finite series are found in a closed-form.


  • . (correct)

  • .

  • .

 More >>


April 9, 2009
Some Finite Series Help to Find a Family of Machin-Type Formula
For each positive integer n,

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