Asymptotics and Special Functions
eBook - PDF

Asymptotics and Special Functions

  1. 588 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Asymptotics and Special Functions

About this book

Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.

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Yes, you can access Asymptotics and Special Functions by F. W. J. Olver, Werner Rheinbolt in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2014
Print ISBN
9780125258500
eBook ISBN
9781483267449
Topic
Mathematics
Subtopic
Calculus
Index
Mathematics

Table of contents

  1. Front Cover
  2. Asymptotics and Special Functions
  3. Copyright Page
  4. Table of Contents
  5. Dedication
  6. PREFACE
  7. CHAPTER 1. INTRODUCTION TO ASYMPTOTIC ANALYSIS
  8. CHAPTER 2. INTRODUCTION TO SPECIAL FUNCTIONS
  9. CHAPTER 3. INTEGRALS OF A REAL VARIABLE
  10. CHAPTER 4. CONTOUR INTEGRALS
  11. CHAPTER 5. DIFFERENTIAL EQUATIONS WITH REGULAR SINGULARITIES; HYPERGEOMETRIC AND LEGENDRE FUNCTIONS
  12. CHAPTER 6. THE LIOUVILLE-GREEN APPROXIMATION
  13. CHAPTER 7. DIFFERENTIAL EQUATIONS WITH IRREGULAR SINGULARITIES; BESSEL AND CONFLUENT HYPERGEOMETRIC FUNCTIONS
  14. CHAPTER 8. SUMS AND SEQUENCES
  15. CHAPTER 9. INTEGRALS: FURTHER METHODS
  16. CHAPTER 10. DIFFERENTIAL EQUATIONS WITH A PARAMETER: EXPANSIONS IN ELEMENTARY FUNCTIONS
  17. CHAPTER 11. DIFFERENTIAL EQUATIONS WITH A PARAMETER: TURNING POINTS
  18. CHAPTER 12. DIFFERENTIAL EQUATIONS WITH A PARAMETER: SIMPLE POLES AND OTHER TRANSITION POINTS
  19. CHAPTER 13. CONNECTION FORMULAS FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS
  20. CHAPTER 14. ESTIMATION OF REMAINDER TERMS
  21. ANSWERS TO EXERCISES
  22. REFERENCES
  23. INDEX OF SYMBOLS
  24. GENERAL INDEX