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Wallis-Ramanujan-Schur-Feynman

2010; Taylor & Francis; Volume: 117; Issue: 7 Linguagem: Inglês

10.4169/000298910x496741

1930-0972

Tewodros Amdeberhan, Olivier Espinosa, V. H. Moll, Armin Straub,

Advanced Mathematical Theories and Applications

One of the earliest examples of analytic representations for π is given by an infinite product provided by Wallis in 1655. The modern literature often presents this evaluation based on the integral formula In trying to understand the behavior of this integral when the integrand is replaced by the inverse of a product of distinct quadratic factors, the authors encounter relations to some formulas of Ramanujan, expressions involving Schur functions, and Matsubara sums that have appeared in the context of Feynman diagrams. Additional informationNotes on contributorsT. AmdeberhanTEWODROS AMDEBERHAN received his Ph.D. in mathematics from Temple University under the supervision of Doron Zeilberger. His main interest lies in WZ-theory, number theory, and elliptic PDEs. He has been a visiting scholar at Princeton and MIT. Currently, he teaches at Tulane University and holds a permanent membership at DIMACS, Rutgers University. In his spare time he enjoys playing chess and soccer.O. EspinosaOLIVIER ESPINOSA was born in Valparaiso, Chile. He received a Ph.D. in particle physics from Caltech in 1990, and joined the faculty of Universidad Tecnica Federico Santa Maria in Valparaiso in 1992, where he is now professor of physics. Although his main area of research has been quantum field theory, since 2000 he has also mantained a fruitful collaboration with Victor H. Moll of Tulane University on the pure mathematics of some integrals and infinite sums connected with the Hurwitz zeta function. Olivier is married to Nina and is the father of two college-aged children.V. H. MollVICTOR H. MOLL is a professor of mathematics at Tulane University. He studied under Henry McKean at the Courant Institute of New York University. In the last decade of the last century, through the influence of a graduate student (George Boros), he entered the world of Integrals. Before coming to Tulane, he spent two years at Temple University in Philadelphia, where he was unknowingly coached by Donald J. Newman. He enjoys collaborating with students and anyone interested in the large variety of topics related to the evaluation of integrals. In his spare time, he enjoys the wonderful things that New Orleans has to offer: great music and fantastic food.A. StraubARMIN STRAUB received one of the last classic diplomas from Technische Universität Darmstadt, Germany, in 2007 under the guidance of Ralf Gramlich. At the moment, he is pursuing his Ph.D. at Tulane University, New Orleans, where his appetite for combinatorics, special functions, and computer algebra is constantly nurtured by his advisor Victor Moll. Besides mathematics of almost all sorts he is excited about currently teaching his first course, and particularly enjoys eating and playing soccer.