What Might "Understand a Function" Mean?

Authors:
James H. Davenport
Affiliations:
Department of Computer Science, University of Bath, Bath BA2 7AY, England
Venue:
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Year:
2007

Citing 14
Cited 1

Integration in Finite Terms with Special Functions: the Error Function

Journal of Symbolic Computation
An algorithm for solving second order linear homogeneous differential equations

Journal of Symbolic Computation
Integration in finite terms with special functions: the logarithmic integral

SIAM Journal on Computing
Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients

Journal of Symbolic Computation
Integration of a class of transcendental Liouvillian functions with error-functions, part I

Journal of Symbolic Computation
Integration of a class of transcendental Liouvillian functions with error-functions, part II

Journal of Symbolic Computation
A conjecture on integration in finite terms with elementary functions and polylogarithms

ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Function evaluation on branch cuts

ACM SIGSAM Bulletin
Towards a general theory of special functions

Communications of the ACM
“According to Abramowitz and Stegun” or arccoth needn't be uncouth

ACM SIGSAM Bulletin - Special issue of OpenMath
Equality in computer algebra and beyond

Journal of Symbolic Computation - Integrated reasoning and algebra systems
y'+ fy = g

EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
ESF: an automatically generated encyclopedia of special functions

ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Adherence is better than adjacency: computing the Riemann index using CAD

Proceedings of the 2005 international symposium on Symbolic and algebraic computation

Understanding branch cuts of expressions

CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Many functions in classical mathematics are largely defined in terms of their derivatives, so Bessel's function is "the" solution of Bessel's equation, etc. For definiteness, we need to add other properties, such as initial values, branch cuts, etc. What actually makes up "the definition" of a function in computer algebra? The answer turns out to be a combination of arithmetic and analytic properties.