# Mathematics Colloquium | Gaurav Bhatnagar

## November 2 @ 4:30 pm - 5:30 pm

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### Event Details

SpeakerGaurav Bhatnagar

Visiting Associate Professor, Ashoka University

Title: Telescoping continued fractions for the error term in Stirling’s formula

Abstract: We calculate the error term $r_n$ in Stirling’s approximation

$$n! = \sqrt{2\pi}n^{n+1/2}e^{-n}e^{r_n},$$ giving one approach to a problem considered by Stirling in 1730. This is an extension of Robbin’s (1955) idea and shows how to better previous lower bounds for $r_n$ given by Ces\`{a}ro (1922), Nanjundiah (1959), Maria 1965), and Popov (2008). Our approach is elementary and algorithmic and uses continued fractions.

This is ongoing joint research with Krishnan Rajkumar (JNU).

In this talk, we will first outline Robbin’s proof of Stirling’s formula.  The talk should be accessible to students.

The talk will be recorded but not broadcast live, because we present some unpublished ideas. It may be available online later.

About the Speaker: Gaurav Bhatnagar obtained his Ph.D. in Mathematics from The Ohio State University in 1995. After his Ph.D., he spent one year each at Ohio State and the Indian Statistical Institute, Delhi. Subsequently, he joined the educational technology industry, where he has been able to make a significant contribution to the teaching and learning processes of Indian schools. Since September 2015, he has been a post-doctoral researcher in various institutions, including ISI, Delhi; the Faculty of Mathematics at the University of Vienna; and, the School of Physical Sciences (SPS), JNU. Currently he is Visiting Associate Professor, Ashoka University.

He has co-edited (with Sugata Mitra and Shikha Mehta) An Introduction to Multimedia Systems (Academic Press, 2002) and written Get Smart: Maths Concepts (Penguin, 2008), a book on middle school mathematics.

His research interests are in Combinatorics and Special Functions, more specifically, hypergeometric, q-hypergeometric, and elliptic hypergeometric series, their multiple series extensions over root systems, continued fractions, orthogonal polynomials, partitions and elementary number theory. He is also interested in providing a discovery approach to Ramanujan’s identities.

### Details

Date:
November 2
Time:
4:30 pm - 5:30 pm

### Organizer

Department of Mathematics

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