**Contemporary Mathematics**

Volume: 517;
2010;
413 pp;
Softcover

MSC: Primary 05; 11; 14; 15; 37; 65; 68;

Print ISBN: 978-0-8218-4869-2

Product Code: CONM/517

List Price: $115.00

Individual Member Price: $92.00

**Electronic ISBN: 978-0-8218-8196-5
Product Code: CONM/517.E**

List Price: $115.00

Individual Member Price: $92.00

# Gems in Experimental Mathematics

Share this page *Edited by *
*Tewodros Amdeberhan; Luis A. Medina; Victor H. Moll*

These proceedings reflect the special session on Experimental Mathematics held January 5, 2009, at the Joint Mathematics Meetings in Washington, DC as well as some papers specially solicited for this volume.

Experimental Mathematics is a recently structured field of Mathematics that uses the computer and advanced computing technology as a tool to perform experiments. These include the analysis of examples, testing of new ideas, and the search of patterns to suggest results and to complement existing analytical rigor.

The development of a broad spectrum of mathematical software
products, such as *Mathematica*® and *Maple*™,
has allowed mathematicians of diverse backgrounds and interests to use
the computer as an essential tool as part of their daily work
environment.

This volume reflects a wide range of topics related to the young field of Experimental Mathematics. The use of computation varies from aiming to exclude human input in the solution of a problem to traditional mathematical questions for which computation is a prominent tool.

#### Table of Contents

# Table of Contents

## Gems in Experimental Mathematics

- Contents v6 free
- Preface vii8 free
- The art of finding Calabi-Yau differential equations. Dedicated to the 90-th birthday of Lars Gårding 110 free
- A note on a question due to A. Garsia 1928
- Experimental computation with oscillatory integrals 2534
- Experimental mathematics and mathematical physics 4150
- An extension of the parallel Risch algorithm 5968
- Appell polynomials and their zero attractors 6978
- Congruences for Stirling numbers of the second kind 97106
- Expressions for harmonic number exponential generating functions 113122
- Theory of log-rational integrals 127136
- A new algorithm for the recursion of hypergeometric multisums with improved universal denominator 143152
- The method of brackets. Part 2: Examples and applications 157166
- History of the formulas and algorithms for π 173182
- A matrix form of Ramanujan-type series for 1/π 189198
- An algorithmic approach to the Mellin transform method 207216
- Eliminating human insight: An algorithmic proof of Stembridge’s TSPP theorem 219228
- Towards the Koch snowflake fractal billiard: Computer experiments and mathematical conjectures 231240
- An experimental mathematics perspective on the old, and still open, question of when to stop? 265274
- The distance to an irreducible polynomial 275284
- Square roots of 2 × 2 matrices 289298
- On a series of Ramanujan 305314
- Finite analogs of Szemerédi’s theorem 313322
- Towards an automation of the circle method 321330
- The greatest common divisor of an − 1 and bn − 1 and the Ailon-Rudnick conjecture 339348
- Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463). Part II 349358
- Experimentation at the frontiers of reality in Schubert calculus 365374
- On Sp4 modularity of Picard-Fuchs differential equations for Calabi-Yau threefolds 381390

#### Readership

Graduate students and research mathematicians interested in computational aspects of mathematics.