Orders of infinity

By M. Potter. 2004

100 citations recorded by the source corpus.

Subfields: Experimental and Cognitive Psychology, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/a1843a92bd669b003ea016cfae4daa6d51a99d54

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Experimental and Cognitive Psychology

1. Gerald A. Edgar
2. Yaroslav D. Sergeyev
3. Nikos Frantzikinakis

In Geometry and Topology

1. Gerald A. Edgar
2. Yaroslav D. Sergeyev
3. Nikos Frantzikinakis
4. Q. Chu
5. Peter Sarnak

In Theoretical Computer Science

1. Gerald A. Edgar
2. Yaroslav D. Sergeyev
3. Nikos Frantzikinakis

Citations in the corpus

• Some open problems on multiple ergodic averages (2011, methodology): “An explicit example of a Hardy field to keep in mind is the set LE that consists of all logarithmic-exponential functions (introduced by Hardy in [179]), meaning all functions defined on some half-line (c,∞) using a finite combination of the symbols +,−,×, :, log, exp, operating on the real variable”
• Transseries for beginners (2008, methodology): “The development is entirely formal; the analytic aspects and origins of the subject (computer algebra limit algorithms, Écalle’s generalization of Borel summation, Hardy fields, etc.) are omitted—a survey of that aspect of the subject would warrant a separate paper.”
• Abelian integrals and limit cycles (2006, unknown): “We first introduce a precise notion of Chebyshev asymptotic scale of functions that we shall simply call asymptotic scale of functions (for general and basic results about asymptotic scale of functions, see [3,7]):”
• Multiple recurrence and convergence for hardy sequences of polynomial growth (2009, methodology): “An explicit example of a Hardy field to keep in mind is the set LE that consists of all logarithmico-exponential functions ([23], [24]), meaning all functions defined on some halfline (c,∞) using a finite combination of the symbols +,−,×, :, log, exp, operating on the real variable t and on real con”
• Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems (2017, background): “Even though there exist codes allowing one to work symbolically with 1 and other symbols related to the concepts of infinity and infinitesimals, traditional computers work numerically only with finite numbers and situations where the usage of infinite or infinitesimal quantities is required are stud”