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Main SMS (2012)

Brief Notice - We are no longer going to support this website after 2012. Why?  All the information on this website will be kept as it is.
 


 
December 30, 2012

A Special Series Involving Gamma Function

We found a new special series formula in connect with Gamma function Γ(x)For real x,  

 

,

where 36x3k3 - 7xk  ±  1 ≠ 0, k = 1,2,3, ... .

 

It may be rewritten in the form

 

,

 

where x < -1/2 or x > 1/2.

 

August 02, 2012

A Special Series

,

where is the digamma function that is defined.

 

July 29, 2012

Some Special Series

  • ,

where , and are the Zeta constants.

 

June 2, 2012

A Closed Form of Special Value of Gamma Function

, where m is a positive integer.

 

May 20, 2012

A Special Limit Expression Involving Gamma Function

,

where x is real.

 

January 05, 2012

New Formula of Gamma function Approximation 

The Gamma function approximation gives a high level of accuracy for real x, 

Notes

1. the natural logarithm of the Gamma function on the left hand side.

2. In mathematics, the Gamma function is an important function that many other special functions depend on. If the closed-form of

Gamma function is found, the chance of resolving the Riemann hypothesis is very high.  Unfortunately, its existence is still not known.

 

View this formula in MathML for XHTML editing

 


I do not know how and when the numbers are created.   I only know that numbers are already made available in the structures of nature in which each set number being associated with a structure represents a cold beauty in such a way that has been profoundly designed and eternally engraved in timeless patterns. (T.V.