Experimental Mathematics is a recently structured field of Mathematics that uses a computer and advanced computing technology as tools to perform experiments such as analysis of examples, testing of new ideas, and the search of patterns. The development of a broad spectrum of mathematical software products such as MathematicaR and MapleTM has allowed mathematicians of diverse backgrounds and interests to make the computer an essential part of their daily working environment. This volume represents the AMS Special Session on Experimental Mathematics held in January 2007 in New Orleans. This gathering is part of an annual meeting of a growing number of scientists that have been labeled experimental mathematicians. The guiding principles of the field, some of which are included in the introduction to these proceedings, are similar to those of laboratory experiments in the physical and biological sciences.
Two dimensional directed lattice walks with boundaries Arvind Ayyer Ayyer, Arvind Doron Zeilberger Zeilberger, Doron 1
Computer-assisted discovery and proof David H. Bailey Bailey, David H. Jonathan M. Borwein Borwein, Jonathan M. 21
On the collection of integers that index the fixed points of maps on the space of rational functions Curtis D. Bennett Bennett, Curtis D. Edward Mosteig Mosteig, Edward 53
Questionable claims found in Ramanujan's lost notebook Bruce C. Berndt Berndt, Bruce C. O-Yeat Chan Chan, O-Yeat Sung-Geun Lim Lim, Sung-Geun Alexandru Zaharesou Zaharesou, Alexandru 69
Partition polynomials: Asymptotics and zeros Robert P. Boyer Boyer, Robert P. William M. Y. Goh Goh, William M. Y. 99
Hypergeometric functions related to series acceleration formulas David M. Bradley Bradley, David M. 113
Using integer relations algorithms for finding relationships among functions Marc Chamberland Chamberland, Marc 127
Conjecturing the optimal order of the components of the Li/Keiper constants Mark W. Coffey Coffey, Mark W. 135
An experimental approach to equation-solving: Symmetry and dynamics Scott Crass Crass, Scott 161
Multidimensional radix representations and Hot Spot Theorem Eva Curry Curry, Eva 181
Some properties of the inverse error function Diego Dominici Dominici, Diego 191
On the Laplace transform of the Psi function M. Lawrenoe Glasser Glasser, M. Lawrenoe Dante Manna Manna, Dante 205
Computer algebra for special function inequalities Manuel Kauers Kauers, Manuel 215
An isodiametric problem for equilateral polygons Michael J. Mossinghoff Mossinghoff, Michael J. 237
Some Euler-type integrals and a new rational series for Euler's constantOlivier Oloa Oloa, Olivier 253
Disturbing the q-Dyson conjecture Andrew V. Sills Sills, Andrew V. 265
Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463) Jonathan Sondow Sondow, Jonathan Kyle Schalm Schalm, Kyle 273
Symbol-crunching with the gambler's ruin problem Doron Zeilberger Zeilberger, Doron 285
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More About This Textbook
Overview
Experimental Mathematics is a recently structured field of Mathematics that uses a computer and advanced computing technology as tools to perform experiments such as analysis of examples, testing of new ideas, and the search of patterns. The development of a broad spectrum of mathematical software products such as MathematicaR and MapleTM has allowed mathematicians of diverse backgrounds and interests to make the computer an essential part of their daily working environment. This volume represents the AMS Special Session on Experimental Mathematics held in January 2007 in New Orleans. This gathering is part of an annual meeting of a growing number of scientists that have been labeled experimental mathematicians. The guiding principles of the field, some of which are included in the introduction to these proceedings, are similar to those of laboratory experiments in the physical and biological sciences.
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Table of Contents
Two dimensional directed lattice walks with boundaries Arvind Ayyer Ayyer, Arvind Doron Zeilberger Zeilberger, Doron 1
Computer-assisted discovery and proof David H. Bailey Bailey, David H. Jonathan M. Borwein Borwein, Jonathan M. 21
On the collection of integers that index the fixed points of maps on the space of rational functions Curtis D. Bennett Bennett, Curtis D. Edward Mosteig Mosteig, Edward 53
Questionable claims found in Ramanujan's lost notebook Bruce C. Berndt Berndt, Bruce C. O-Yeat Chan Chan, O-Yeat Sung-Geun Lim Lim, Sung-Geun Alexandru Zaharesou Zaharesou, Alexandru 69
Partition polynomials: Asymptotics and zeros Robert P. Boyer Boyer, Robert P. William M. Y. Goh Goh, William M. Y. 99
Hypergeometric functions related to series acceleration formulas David M. Bradley Bradley, David M. 113
Using integer relations algorithms for finding relationships among functions Marc Chamberland Chamberland, Marc 127
Conjecturing the optimal order of the components of the Li/Keiper constants Mark W. Coffey Coffey, Mark W. 135
An experimental approach to equation-solving: Symmetry and dynamics Scott Crass Crass, Scott 161
Multidimensional radix representations and Hot Spot Theorem Eva Curry Curry, Eva 181
Some properties of the inverse error function Diego Dominici Dominici, Diego 191
On the Laplace transform of the Psi function M. Lawrenoe Glasser Glasser, M. Lawrenoe Dante Manna Manna, Dante 205
Computer algebra for special function inequalities Manuel Kauers Kauers, Manuel 215
An isodiametric problem for equilateral polygons Michael J. Mossinghoff Mossinghoff, Michael J. 237
Some Euler-type integrals and a new rational series for Euler's constantOlivier Oloa Oloa, Olivier 253
Disturbing the q-Dyson conjecture Andrew V. Sills Sills, Andrew V. 265
Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463) Jonathan Sondow Sondow, Jonathan Kyle Schalm Schalm, Kyle 273
Symbol-crunching with the gambler's ruin problem Doron Zeilberger Zeilberger, Doron 285