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,

.

The formula can be rewritten in the form

,

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

 

August 02, 2012

A Special Series

,

where is the digamma function, which is defined as

.

 

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 formula below provides an approximation of the Gamma function, offering a high degree of accuracy for real values of x:

Notes

1. The left-hand side represents the natural logarithm of the Gamma function.

2. In mathematics, the Gamma function is crucial as many other special functions depend on it. Discovering a closed-form solution for the Gamma function would significantly enhance the chances of resolving the Riemann Hypothesis.  Unfortunately, such a closed form remains unknown.

View this formula in MathML for XHTML editing