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Foreword

Published online by Cambridge University Press:  24 November 2009

George Gasper
Affiliation:
Northwestern University, Illinois
Mizan Rahman
Affiliation:
Carleton University, Ottawa
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Summary

My education was not much different from that of most mathematicians of my generation. It included courses on modern algebra, real and complex variables, both point set and algebraic topology, some number theory and projective geometry, and some specialized courses such as one on Riemann surfaces. In none of these courses was a hypergeometric function mentioned, and I am not even sure if the gamma function was mentioned after an advanced calculus course. The only time Bessel functions were mentioned was in an undergraduate course on differential equations, and the only thing done with them was to find a power series solution for the general Bessel equation. It is small wonder that with a similar education almost all mathematicians think of special functions as a dead subject which might have been interesting once. They have no idea why anyone would care about it now.

Fortunately there was one part of my education which was different. As a junior in college I read Widder's book The Laplace Transform and the manuscript of its very important sequel, Hirschman and Widder's The Convolution Transform. Then as a senior, I. I. Hirschman gave me a copy of a preprint of his on a multiplier theorem for Legendre series and suggested I extend it to ultraspherical series. This forced me to become acquainted with two other very important books, Gabor Szego′'s great book Orthogonal Polynomials, and the second volume of Higher Transcendental Functions, the monument to Harry Bateman which was written by Arthur Erdélyi and his co-workers W. Magnus, F. Oberhettinger and F. G. Tricomi.

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Publisher: Cambridge University Press
Print publication year: 2004

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  • Foreword
  • George Gasper, Northwestern University, Illinois, Mizan Rahman, Carleton University, Ottawa
  • Book: Basic Hypergeometric Series
  • Online publication: 24 November 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511526251.001
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  • Foreword
  • George Gasper, Northwestern University, Illinois, Mizan Rahman, Carleton University, Ottawa
  • Book: Basic Hypergeometric Series
  • Online publication: 24 November 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511526251.001
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Foreword
  • George Gasper, Northwestern University, Illinois, Mizan Rahman, Carleton University, Ottawa
  • Book: Basic Hypergeometric Series
  • Online publication: 24 November 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511526251.001
Available formats
×