Abel Binomial Theorems

I remember seeing at least 5 binomial theorems of Niels Abel. But internet works in a funny way. I do not see those pages now. 

I now managed to get two of Abel's many binomial theorems. 

They are

Have a nice day !!

Thank you Wolfram Alpha

I am thankful to Wolfram Alpha more than anything. It was Wolfram Alpha which guided me in my mathematical journey.

The results I am talking of are

Thank you Wolfram Alpha for everything !!

Masala dosa

 

Masala dosa is a thin pancake of rice and urad dal batter saltish and sourish in taste. It is filled with aloo curry in traditional method. Nowadays the fillings have improved and lot many stuffed dosas are available.  

Then I thought of Gauss Newton algorithm

Then I thought of my basic Rational number series not suitable to Mumbai, allahabad and Chennai Mathematical journals.

Have a nice day !!

Some points

 

Not all calculators support 0.5! 

I believe that the first equation can be true. 

For Putnam aspirants

Putnam is American mathematics olympiad sorts. It is conducted every year. MIT guys do well in these exams.  Indians staying in USA are okayish in these exams. 

Putnam has questions in 

Numbers

Geometry

Functions 

Limits

I wish I become a Putnam coach. There is a lot of money. However I have only intuitions.  No steps. With respect to the above four points on Putnam questions my intuitions are

Consecutive number theory 

3 to 4 Consecutive numbers 

Consecutive number binomial function statement

Star Delta convergence test

You teach me problem solving approach.  I give you intuitions.  How about that?

Anyways. 

Take my intuitions.  I don't have much in hand.

May Allah give me something. 

Have a nice day !!

Bhalla Papdi

 

Bhalla papdi is popular in North India. It is thayir vada and flat pani puris in curd, saunth  and spices.

Then I thought of Gauss-Legendre collaboration in pi and other important functions. 

Then I thought of Rational Series and rejection of the ideas contained therein by JRMS and other journals of India.

Vada Pav

 

Vada Pav is a famous dish in western India. It is aloo bonda between pav. It is served with green chutney.

Then I thought of Euler-Maclaurin formula.

Then I thought of JRMS. There was foundation of binomial using rational number series in my paper submitted. I was told paper rejected due to quality.

My good wishes shall always be there.

Particularly, the above expression has been rejected by JRMS for lack of sufficient quality.

I later got the expression published in IJMT.