Generalized Associated Legendre Functions And Their Applications
eBook - PDF

Generalized Associated Legendre Functions And Their Applications

  1. 216 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Generalized Associated Legendre Functions And Their Applications

Book details
Table of contents
Citations

About This Book

The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all classical hypergeometric functions such as the well-known Gaussian hypergeometric functions, the Bessel, Macdonald, Legendre, Whittaker, Kummer, Tricomi and Wright functions, the generalized hypergeometric functions ?Fq, Meijer's G-function, Fox's H-function, etc.Application of the new special functions allows one to increase considerably the number of problems whose solutions are found in a closed form, to examine these solutions, and to investigate the relationships between different classes of the special functions.This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, Pm,n?(z) and Qm,n?(z), which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legnedre functions as their series representations, asymptotic formulas in a neighborhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions.The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions Pm,n?(z) and Qm,n?(z), the classes of dual and triple integral equations associated with the function Pm,n-1/2+i?(ch?) etc.

Frequently asked questions

Simply head over to the account section in settings and click on “Cancel Subscription” - it’s as simple as that. After you cancel, your membership will stay active for the remainder of the time you’ve paid for. Learn more here.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Both plans give you full access to the library and all of Perlego’s features. The only differences are the price and subscription period: With the annual plan you’ll save around 30% compared to 12 months on the monthly plan.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes, you can access Generalized Associated Legendre Functions And Their Applications by Iryna Fedotova, Nina Virchenko in PDF and/or ePUB format, as well as other popular books in Biological Sciences & Science General. We have over one million books available in our catalogue for you to explore.

Information

Publisher
World Scientific
Year
2001
ISBN
9789812811783
Topic
Biological Sciences
Subtopic
Science General
Index
Biological Sciences

Table of contents

  1. Contents
  2. Foreword
  3. Preface
  4. §1. A general information on Legendre functions
  5. §2. The generalized associated Legendre functions
  6. §3. The series representations of the generalized associated Legendre functions
  7. §4. Relations between different solutions of the generalized Legendre equation. Wronskians of linearly independent solutions
  8. §5. Relations between contiguous generalized associated Legendre functions
  9. §6. Differential operators generated by the generalized associated Legendre equation
  10. §7. Asymptotic formulas for the generalized associated Legendre functions in a neighborhood of singular points
  11. §8. Asymptotic representations of the generalized associated Legendre functions as functions of parameters
  12. §9. Integral representations of the generalized associated Legendre functions of the first kind
  13. §10. Integral representations of the generalized associated Legendre functions of the second kind
  14. §11. Zeros of the generalized associated Legendre functions
  15. §12. Connection of the generalized associated Legendre functions with the Jacobi functions
  16. §13. Integral relations and series with the generalized associated Legendre functions
  17. §14. Relations between the generalized associated Legendre functions Bessel functions elliptic integrals and incomplete B-functions
  18. §15. Integral transforms with the generalized associated Legendre functions
  19. §16. Dual integral equations with the generalized Legendre function of the first kind Pm,n -1/2+iτ(chα)
  20. §17. Dual integral equations with Pm,n -1/2+iτ(chα) and the weight function [1 + G(τ)]
  21. §18. Triple integral equations with the generalized Legendre function of the first kind Pm,n -1/2+iτ(chα)
  22. §19. Hybrid dual integral equations
  23. §20. Systems of triple integral equations with the generalized associated Legendre functions of the first kind Pm,n -1/2+iτ(chα)
  24. §21. On a property of the fractional Riemann-Liouville integral of Pm,n k (z)
  25. §22. On some generalized integral operators of Buschman-Erdélyi's type
  26. §23. Factorization of integral operators with the generalized associated Legendre functions and its application for solving integral equations
  27. §24. Some generalizations of integral transforms of Mehler-Fock type and their applications
  28. §25. Examples of the integrals involving the generalized associated Legendre functions
  29. Appendix. The hypergeometric function
  30. Bibliography
  31. Subject index