Argument in favor of 4.666 expressions

 Are complex number factor small i a necessity ?

Not really. The hands sway, the legs sway, the eyes sway but our ears do not sway. Our nose do not sway. Our trunk do not sway. The sway that is implied in i is not essential to understand. 

So I am here propagating the importance of KAAL number 4.666. It is a competitor for e which is 2.718. . . . 

First of all the complete 4.666 expressions. All the three involving 4.666 are approximate expressions.

The first and the third are fine but I hear a lot of rejections for the fourth one, which are approximate integrals. The criticism is mainly on the lower value of the integral.

I would like to defend it by saying that saturation is a nature principle. Many things saturate and stay stable.

Below is a saturation curve.

The lower value of integral is

and its curve is

You may observe that the lower value of integral has a nature approved principle of saturation. Because its curve is similar to saturation curve.

Therefore, I am sticking very deeply to KAAL number or 4.666. I believe this to be a truth of nature and to me the expressions of 4.666 are of nature.

Gamma function from consecutive numbers

I made gamma function from consecutive number function.  It feels great !!

Here are the Wolfram Alpha screenshots.

I have typed the gamma function in MS Word

Have a nice day !!

4.666 based approximate gamma(2n+1)

 I am submitting my almost final submission on 4.666 based approximate gamma(2n+1).

The formula is as given below. Check the big expression in the lower value of the integral.

The Wolfram Alpha screenshots

If only the top think tank in India agrees. We can have the truth (because of gamma function) behind the necessary human understanding of the number 0.

My good wishes for a nice day !!

Mathematics snippets

 Archimedes Pi

Golden Ratios

Combination (2n,n) and more

Sigma based Gamma function

Question and answer in Math GPT

These are what I am currently thinking about. So made a post. I want to correct 4.666 integral and make it closer to gamma function; but am unable to do so.

Have a nice week folks !!

Which one of these gamma functions are correct?

Gamma functions are how humans understand truth in number terms.  One doesn't say there are 5 chairs but we also mean their arrangements,  selection, combinations and all. So saying 5 chairs is poor representation of reality. Functions involving 5! are superior.

Euler made gamma functions.  Nature can calculate 5.45! too. Decimal factorial.  When one says factorial then it means whole numbers.  When gamma functions then decimal factorial too apart from whole numbers.

50000.116!

50000.116! from my Sigma functions. 

50000.116! from a standard formula 

50000.116! from my latest formula 

But why discrepancy and where and what are the errors ?

Only mathematicians can say. I do not know. 

At last !! Got gamma function in terms of Integrals

I was desperate to make a gamma function. Because gamma function are the truth. About 75 percent of nature's truth are hidden in gamma. This is my feeling !!

In my earlier post I wrote gamma function in terms of Sigma operation.

But in this blog post, I am attaching the gamma function in terms of Integral operation.

And the Wolfram screenshots to confirm that the expression is correct.

Have a very nice day, folks !! 

Gamma function is the truth

 Here is a gamma function.

I hope you like it !! Have a nice day !!