This is a continuation of the series of summer projects sponsored by department of science and technology, government of India. In this project work, I have worked to collect and expand what Ramanujan did with Nested Radicals and summarized all important facts into the one article. In the article, there are formulas, formulas and only formulas — I think this is exactly what Ramanujan is known for.

This article not only deals with Ramanujan’s initial work on Nested Radicals but also develops few new models and adds more information to it by catching latest research in a very elementary way. The project was initiated first at gauravtiwari.org, about two years ago and done rigorously in recent days.

Download a PDF copy of the article (here) and let me know what you think about it.

 

Total
0
Shares


Feel free to ask questions, send feedback and even point out mistakes. Great conversations start with just a single word. How to write better comments?
Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

You May Also Like

A Yes No Puzzle

This is not just math, but a very good test for linguistic reasoning. If you are serious about this test and think that you’ve a sharp [at least average] brain then read the statement (only) below –summarize it –find the conclusion and then answer that whether summary of the statement is Yes or No. [And if you’re not serious about…

How many apples did each automattician eat?

Four friends Matt, James, Ian and Barry, who all knew each other from being members of the Automattic, called Automatticians, sat around a table that had a dish with 11 apples in it. The chat was intense, and they ended up eating all the apples. Everybody had at least one apple, and everyone know that fact, and each automattician knew…

Understanding Poincaré Conjecture

Introduction & Statement of Poincaré Conjecture In 1904, the french Mathematician Henri Poincaré posed an epoch-making question in one of his papers, which asked: If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere? Explanation The statement can be explained by considering the analogous two-dimensional situation. Let us think of a rubber band stretched around the…

Fox – Rabbit Chase Problems

Part I: A fox chases a rabbit. Both run at the same speed $ v$ . At all times, the fox runs directly toward the instantaneous position of the rabbit , and the rabbit runs at an angle $ \alpha $ relative to the direction directly away from the fox. The initial separation between the fox and the rabbit is…

Newton’s Trinity College Notebook is Online!

Cambridge Digital Library had made Newton’s exceptionally great works online. Some times ago they added the Trinity College Notebook by Isaac Newton, which he used to teach in the college in 17th century.     Read More About the Project Here. List of other works of Newton can be found at www.newton.ac.uk/newton.html.

Everywhere Continuous Non-differentiable Function

Weierstrass had drawn attention to the fact that there exist functions which are continuous for every value of $ x$ but do not possess a derivative for any value. We now consider the celebrated function given by Weierstrass to show this fact. It will be shown that if $ f(x)= \displaystyle{\sum_{n=0}^{\infty} } b^n \cos (a^n \pi x) \ \ldots (1)…