To avoid confusion

Google blog readers may be confused as to what I mean to say from the Wolfram Alpha screenshots that I have been pasting in my blog posts.

This is what I mean to say. This is the final statement.

Have a nice day !!

This too has pattern

 One of the surprising results I got was of golden ratio and pi equivalence.  Philosophically both are ratios. One equally and the other on God's proportion. 

The difference between the golden ratio and pi expressions was 2 into 3 factorial by 5 factorial.  Which is 1 by combination (5,2).

I decided to use combination (5n,2n) and explore more.

Here are the results. 

As you can see, the patterns are simply amazing.  There is a clear one line pattern difference in them. Is it not amazing?

Hypergeometric functions are of John Wallis. My first pi algorithm was of John Wallis. Measuring Behavior.  Now I am able to show patterns in his Hypergeometric functions. 

John Wallis 

I have taken a printout of the above and have kept in my office drawer.

Have a nice day !!

Another picture with an eternal message

 

Consecutive numbers fetched results in

1. Infinite series and mathematical constants

2. Binomials and approximations

3. Shagun

4. Hypergeometric distributions

Have a nice day !!

A few pictures but an eternal message