And Gamma function

Here is a gamma function.

And the Wolfram Alpha screenshot for 3.75!

Have a nice day !!

Let us recapitulate KAAL number

A lot has been written about KAAL number. There are possibly many confusions because I tried "too much" to make them "accurate". Also I was "hell-bent" on making a gamma function.

This blog post straightens many things.

KAAL number is (Kirtivasan, Abhaya, Akshaya, Lata) number.

Its value is 4.4

I am not doing any gamma equations with KAAL number.

It gives approximate results. Not any of the results are accurate. That is the beauty of KAAL number. Its beauty lies in its approximations.

Write up

I am using a number 67.89 in all the below expressions.

Infinite series RHS

Infinite series LHS

One(x)

Zero(x)

Expression 1

Expression 2

I wanted to finalize my expressions on KAAL number. I am not getting into gamma functions. I am not making 4.4 more accurate.

Goodbye for now !!

Combination now made continuous

The combination formula binomial(n,r) is now made continuous. This means that one need not go back and forth or up and down but keep moving ahead.

Here is the formula and an example with it.

That is why binomial distribution are so natural. It is continuous. 

I feel ecstatic. I hope you like the expression.

Below is the Wolfram Alpha screenshots for binomial(7,2) and binomial(8,3)

Have a nice day !!

Childhood Dreams

Right from my childhood I would wonder why there is no formula for a^n-b^n and a^n+b^n.

I have fulfilled this dream of mine yesterday. It took me whole Sunday to do that. 😄. My mathematical prowess is weak. But my intuitions are okay, I guess.

Here are the formulas.

They are not exactly a^n-b^n and a^n+b^n. But the values can be computed.

Have a nice day, guys !!

Related to KAAL number?

KAAL number is a memory of a few months.  

Yesterday,  I did an expression and got 1 by e. Today,  I tried the same expression with alternate negation.  I got 0.216. And inverse of 0.216 is about the same value as KAAL number. 

This is interesting. 

1 by e

 I was thinking about something, when the expression on the LHS, came into my mind. I wanted to find out whether the expression on LHS results in something good.

Yes, the expression results in 1 by e.

And below is the Wolfram Alpha screenshot to confirm that the expression is indeed 1 by e.

Have a nice day. Have a nice weekend !!

Three ways to look at my drawing objectives

There are three ways to look at my drawing objectives which are to be achieved in 2 years time.

First way - To draw like masters

Second way - To achieve perfection in pencil control

Third way - To reach art level 80 in the eyes of AI.

Of course,  I shall be working on still life drawings,  outdoor drawings,  comic drawing and cartoons and portraits.  But above are the improvement plans.

I hope you have understood my expectations from myself. 

Weekend is nearing. Have a great weekend,  guys !!