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Asymptotic forms of Whittaker’s confluent hypergeometric functions

About this Title

A. Erdélyi and C. A. Swanson

Publication: Memoirs of the American Mathematical Society
Publication Year: 1957; Number 25
ISBNs: 978-0-8218-1225-9 (print); 978-0-8218-9967-0 (online)
DOI: https://doi.org/10.1090/memo/0025
MathSciNet review: 0090678

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Table of Contents

Chapters

  • 1. Introduction
  • 2. Confluent hypergeometric functions
  • 3. Bessel functions
  • 4. Airy functions
  • 5. The Bessel comparison functions
  • 6. The functions $U$ and $T$
  • 7. Asymptotic forms for the functions $u_r$ and $u_r’$
  • 8. The Airy comparison functions
  • 9. Asymptotic forms for the functions $v_r$ and $v_r’$
  • 10. Asymptotic forms for Whittaker functions
  • 11. Asymptotic forms for Coulomb wave functions
  • 12. Simplified asymptotic forms for restricted $x$-intervals