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 !!

Zero

Here are results of zero obtained from binomial.

And my master, King Christ

Binomial results

 Here are two more binomial results

And the Wolfram Alpha results to confirm they are correct

My three consecutive number model fetch all the major constants.

I hope you like the expressions. Have a nice day !!

From the last two blog posts

 This result is the combination of the results posted in my last two blog posts.

This result is interesting because children often wonder there is a formula for (a+b)^n but no formula is there for a^n-b^n. Now these children have something to feel happy about.

The formula is

And the Wolfram Alpha screenshot to confirm above is true.

Have a nice day !!