Advanced KAAL number theory development

 I plan to do my own research in advanced KAAL number theory development. KAAL number stands for (Kirtivasan, Abhaya, Akshaya, Lata) number.

The advanced KAAL number theory development is not changing 4.4 to something else. It is not changing the basic formula structures. It is not changing any structure of one(x) or zero(x) . But advanced KAAL number theory is about changing the p structure.

You may recall p from below.

Interesting results are there when we treat p as an infinite series. There are three results which are interesting.

The second one is what is the present p from.1/x^0 plus 2/x^1 plus 3/x^2.

Have a nice weekend, folks !!

And Finally

From 2024, I was mad with KAAL number. I was interested in approximate formula for (2n)! and I went to greater heights to know a mathematical truth.

I worked with Wolfram Alpha and kept moving onwards. KAAL number theory kept my mind occupied more than pi, phi, binomials and combination(2n,n). I kept moving ahead.

I would like to state here that KAAL number theory is due to an experiment. An observation. You may be aware that I have done experiments in Number Theory and in this blog I have made an Experiments tag too.

I expected help from mathematicians. Help from Institutes. But I was rejected .

In this blog post I am stating my FINAL KAAL number results.

The gamma function is actually an e function. Just changed it to suit 4.4.

Have a nice weekend guys !!

Spending time

You may be aware that I stay in Ranchi with my mother. And I have 4 hours time with me. Daily. 

I spent time in expressions with Wolfram Alpha.  But not anymore.  Because expressions have dried up.

I now plan to spend time on drawing on digital. Drawing practices on paper. Harmonium. 

Hope Lord Jesus helps me in spending time thus.

Have a nice day!!

Approximate gamma values

 

And Wolfram screenshots to confirm the correctness

I wanted to build Indian gamma function. But my KAAL number gave only approximate results. But here in I am able to show approximate gamma function. This is truly a very happy day for me. Mathematics is not my pride. Not my ego. But my lifestyle. I rely on my mathematics a lot. To guide myself. This is the way I lead my life. And today I made approximate gamma function. In integral form.

I am finished with KAAL number discussions. And blog posts.

Approximate division by three consecutive numbers

 Here is an approximate division formula. The below divides n by m.

And the Wolfram Alpha screenshot for 1475 by 14.75

Hope you like the expression !!

It ain't over with KAAL number theories

KAAL number theories ain't over yet.

I propose a factor p, defined as below. I propose using p just like mathematicians used i in e, cos, sin formulas.

Here's how, I propose the theory

I have checked the results for x equal to 16, 108, 618 and 1618. The results are satisfactory to me.

Have a nice day, guys !!

With a sample seed of x equal to 227

With a sample seed of x equal to 7

With a sample seed of x equal to 8698

Are these fine ?

After much consideration

4.4 is KAAL number.  KAAL stands for (Kirtivasan,  Abhaya,  Akshaya,  Lata).

More digits to above needs discussion.