God made the natural numbers; all the rest is the work of man.      - Leopold Kronecker

The purpose of Series Math Study (SMS) website is to explore and develop the beauty of series formulas that have connections to special mathematical constants.  Most of the series in this website are found with completed proofs.  Some series can be used to calculate ever more accurate values of some special math constants as the desire that has challenged mathematicians for many centuries.

I am ashamed to tell you to how many figures I carried these computations, having no other business at the time.

Issac Newton, personal journal, 1666

(September 17, 2006)

1.

2.

(August 25, 2006)

GraphFunc is an online program for drawing graphs of basic mathematical functions in 2D and 3D coordinate systems.  Click here to use this tool.

(August 1, 2006)

1.

2. The new fast convergent series is found for computing the constant log 2.

(July 4, 2006)

(Twin series – when comparing this series and the one shown below)

(May 29, 2006)

A fast convergent series of BPP-type formulas has been found and can be used for computing the n-th digit ofin base 4096 without computing any prior digits. 

.

(We do not know whether this series is new)

(May 28, 2006)

1. 

2. 

(This series has been found and can be used to compute directly the n-th digit of ln(7) without computing any prior digits. Notice that the base of this series is 729.)

(May 23, 2006)

(May 15, 2006)

1. 

2. 

(April 21, 2006)

(March 7, 2006)

or it can be written in product form:

.

(March 6, 2006)

or it can be written in product form:, which is

.

(March 4, 2006)

, where is the Euler constant.

(January 16, 2006)

1.  (new?),  whereis Apéry’s constant.

2.  (new?)

3. (new?)

4. (new?)

5. (a beautiful series.  This series can be found in Ramanujan’s second notebook)

6. 

Previous Page Next Page

Return SMS

Copyright 2005- www.seriesmathstudy.com.  All rights reserved. Contact us.