Tuesday, March 1, 2022

A general pi pattern

I have attempted a general pi pattern.


Hope you like it !! Have a nice day!!

Replace 2^n with 2^k.

The RHS will change. However the pattern is not yet established. I don't have a pattern.

Added on March 5, 2022

This expression below gives a relationship to what I have been trying. The result on RHS are in the form of gamma functions and root pi.



7 comments:

Kirtivasan Ganesan said...

I think there is an error.
The numerator must be (2^(n+1))^2 instead of (n+1)^2 as written.

Kirtivasan Ganesan said...

Lemma was a new word till a few years back.
Lemma is an intermediate theorem.
The above is a Lemma.
So is the earlier one.
Then there is a statement. An infinite series for 1 has to have all the numbers of the universe. This could also be a Lemma.
Some more expressions of mine can be lemmas.

Kirtivasan Ganesan said...

Hey guys!! I had a brief realization of Khinchin constant also.
Years back.
Made a blog post too. Need to take a relook.
That leaves 3 more nature blessed constants to realize.
Feigenbaum, Madelung and Chaitin constants.

Kirtivasan Ganesan said...

Sir Andrew Wiles got Abel prize, Copley medal. And he was knighted too.
I read that he has written a large book which needs to be read just to understand his proof of Fermat last theorem.

Kirtivasan Ganesan said...

My deepest regards and respect to Sir Andrew Wiles.
Good bye folks!!

Pooja Mahimkar said...

Would be nice if you explain also no? I can't understand a thing

Kirtivasan Ganesan said...

Pooja Madam, I am not getting it.
No great thing. Just typing out some of the expressions on Wolfram Alpha. So Wolfram Alpha is the big key in all these.
It is about convergence. 1/1+1/2+1/3+. . . . does not converge. But 1/1 squared+ 1/2 squared+ 1/3 squared+. . . . . converges.
I have some intuitions about convergence. Probably have a knack.That's all