Start
 
Research + Papers
   
CV
   
 
 
 
 
 



 


Formula Gallery

Here are some formulas arising from the theory of Fractional Sums that I did as a teenager. Now I see them as some kind of art - beautiful, but probably useless. :-)
Most formulas seem to be new, but some are well-known - notably the first one, which has been proved by Euler and Ramanujan before.

If you are interested in the proofs, look here or there.

Here is a product with an irrational number of terms:

The number isn't the only interesting summation boundary:

Note that =.577215... is the Euler-Mascheroni constant, =.91596... is the Catalan constant, and denotes the Riemann and Hurwitz Zeta functions.

Some identities can also be written classically:


In this expression, denotes the Glaisher-Kinkelin constant.

 

Here is another strange limit identity:


Some more fractional product identities:

(The constant=.072815... is one of the Stieltjes constants.)

Something complex and polylogarithm-related:

This is related to Barnes' double Gamma function