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Main SMS (2010)

The followings are outlines and brief notes of the series formulas that have been developed and found recently.
 
October 19, 2010

Gamma Function Approximation Formula (6 decimal places)

The following formula is the Gamma function approximation that provides a high level of accuracy. It gives the value of Gamma function to 6 decimal places of precision for real x < 10, namely

 

.

 

 (Notice, the exponential function is written as exp(x) or ex. This formula is also expressed in terms of logarithm to compute complex z.)

 

October 16, 2010

 Two Series are found in Connection with Mathematical constants,

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August 03, 2010

 Two Series in Connection with Mathematical constants

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July 03, 2010

Sums in which the Square Root of Two and Other Constants Appear are Given by 

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June 27, 2010
A Surprising Sum in whichAppears is Given by 

.

 

April 18, 2010
Some Special Infinite Series
  • .

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February 09, 2010
 Sums of Reciprocals of Two-Term Squares Table

 

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Sums of Reciprocals of Two-Term Cubes Table

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January 30, 2010

Series in Limit Form

Given n is a positive integer.  The following series are found in a closed form as n tends to infinity.

 

  • .

  • .

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January 17, 2010

Sequences and Series Art -- A Generic Infinite Series Found Linking Three Special Sequences '2, 30, 420, ...', '15, 209, 2911, ...', and '17, 241, 3361, ...' with the Constant

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January 08, 2010
Two Beautiful Series in Connection with zeta and Pi Constants 

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January 01, 2010

A Curious Series in Connection with Euler-Mascheroni, Pi Constants 

For positive integer n,

, whereis Euler-Mascheroni constant.

The above series can be transformed into another form, namely

.

 

Another curious series is found in connection to Pi

.

 

(Happy New Year 2010)

 

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Go down deep enough into anything and you will find mathematics. (Dean Schlicter