Journal Article

On the Specialness of Special Functions (The Nonrandom Effusions of the Divine Mathematician)

Robert W. Batterman

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 58, issue 2, pages 263-286
Published in print June 2007 | ISSN: 0007-0882
Published online May 2007 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axm007
On the Specialness of Special Functions (The Nonrandom Effusions of the Divine Mathematician)

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This article attempts to address the problem of the applicability of mathematics in physics by considering the (narrower) question of what make the so-called special functions of mathematical physics special. It surveys a number of answers to this question and argues that neither simple pragmatic answers, nor purely mathematical classificatory schemes are sufficient. What is required is some connection between the world and the way investigators are forced to represent the world. 1

Introduction

2

Some responses to the question

3

Idealization

4

Airy's equation

5

Stokes on the Airy integral

6

Asymptotic expansions and special functions

7

Special functions and the world

8

Conclusion: special functions and the philosophy of mathematics

Journal Article.  9364 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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