Gems in Experimental Mathematics: AMS Special Session on Experimental Mathematics, January 5, 2009, WashingtonTewodros Amdeberhan, Luis A. Medina, Victor H. Moll American Mathematical Soc., 2010 - 413 ページ 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 MathematicaR and MapleTM, 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. |
目次
A note on a question due to A Garsia | 19 |
Experimental computation with oscillatory integrals | 25 |
Experimental mathematics and mathematical physics | 41 |
An extension of the parallel Risch algorithm | 59 |
Appell polynomials and their zero attractors | 69 |
Congruences for Stirling numbers of the second kind | 97 |
Expressions for harmonic number exponential generating functions | 113 |
Theory of logrational integrals | 127 |
A matrix form of Ramanujantype series for 1π | 189 |
An algorithmic approach to the Mellin transform method | 207 |
Computer experiments | 231 |
An experimental mathematics perspective on the old and still open question | 265 |
Square roots of 2 2 matrices | 289 |
On a series of Ramanujan | 305 |
Towards an automation of the circle method | 321 |
The greatest common divisor of an 1 and bn 1 and the AilonRudnick | 339 |
A new algorithm for the recursion of hypergeometric multisums with improved | 143 |
Examples and applications | 157 |
History of the formulas and algorithms for | 173 |
Experimentation at the frontiers of reality in Schubert calculus | 365 |
On Sp4 modularity of PicardFuchs differential equations for CalabiYau | 381 |
多く使われている語句
algebraic algorithm Amer American Mathematical Society analytic angle arctan asymptotics billiard flow billiard KS binomial Borwein coefficients computation conjecture continued fraction converges corresponding curve defined definition denote differential equation digits dominant zero Doron Zeilberger E-mail address elliptic equivalent Euler evaluation example expansion Experimental Mathematics Fagnano orbit Feynman diagrams find finite first formula fractal geodesic flow given Gröbner basis Hence identity integer integrand irreducible polynomial Koch snowflake kv+1 Lemma linear Math Mathematics Subject Classification matrix Mellin transform method of brackets modulo monodromy multisums notation obtain orbit of KS partitions periodic orbit polygonal prime proof Proposition prove quasiperiodic orbits Ramanujan rational billiard rational functions recurrence relation result Risch algorithm satisfies Schubert calculus Schubert problem Section sequence solutions square roots subsets Theorem theory universal denominator values variables Zeilberger