The Classical Orthogonal Polynomials

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Mathematics
Cover of the book The Classical Orthogonal Polynomials by Brian George Spencer Doman, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Brian George Spencer Doman ISBN: 9789814704052
Publisher: World Scientific Publishing Company Publication: September 18, 2015
Imprint: WSPC Language: English
Author: Brian George Spencer Doman
ISBN: 9789814704052
Publisher: World Scientific Publishing Company
Publication: September 18, 2015
Imprint: WSPC
Language: English

This book defines sets of orthogonal polynomials and derives a number of properties satisfied by any such set. It continues by describing the classical orthogonal polynomials and the additional properties they have.

The first chapter defines the orthogonality condition for two functions. It then gives an iterative process to produce a set of polynomials which are orthogonal to one another and then describes a number of properties satisfied by any set of orthogonal polynomials. The classical orthogonal polynomials arise when the weight function in the orthogonality condition has a particular form. These polynomials have a further set of properties and in particular satisfy a second order differential equation.

Each subsequent chapter investigates the properties of a particular polynomial set starting from its differential equation.

Contents:

  • Definitions and General Properties
  • Hermite Polynomials
  • Associated Laguerre Polynomials
  • Legendre Polynomials
  • Chebyshev Polynomials of the First Kind
  • Chebyshev Polynomials of the Second Kind
  • Chebyshev Polynomials of the Third Kind
  • Chebyshev Polynomials of the Fourth Kind
  • Gegenbauer Polynomials
  • Associated Legendre Functions
  • Jacobi Polynomials
  • General Appendix

Readership: Undergraduate and graduate students.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This book defines sets of orthogonal polynomials and derives a number of properties satisfied by any such set. It continues by describing the classical orthogonal polynomials and the additional properties they have.

The first chapter defines the orthogonality condition for two functions. It then gives an iterative process to produce a set of polynomials which are orthogonal to one another and then describes a number of properties satisfied by any set of orthogonal polynomials. The classical orthogonal polynomials arise when the weight function in the orthogonality condition has a particular form. These polynomials have a further set of properties and in particular satisfy a second order differential equation.

Each subsequent chapter investigates the properties of a particular polynomial set starting from its differential equation.

Contents:

Readership: Undergraduate and graduate students.

More books from World Scientific Publishing Company

Cover of the book Creative Mobile Media by Brian George Spencer Doman
Cover of the book Plant Biosecurity Policy Evaluation by Brian George Spencer Doman
Cover of the book Studying Hong Kong by Brian George Spencer Doman
Cover of the book Methods of Differential Geometry in Classical Field Theories by Brian George Spencer Doman
Cover of the book The Magic Garden of George B and Other Logic Puzzles by Brian George Spencer Doman
Cover of the book Local Zeta Regularization and the Scalar Casimir Effect by Brian George Spencer Doman
Cover of the book China's Economic and Social Problems by Brian George Spencer Doman
Cover of the book Astrophysics and the Evolution of the Universe by Brian George Spencer Doman
Cover of the book Energy by Brian George Spencer Doman
Cover of the book Frontiers in Electronics by Brian George Spencer Doman
Cover of the book Black Holes, Cosmology and Extra Dimensions by Brian George Spencer Doman
Cover of the book Mental Health of a Nation by Brian George Spencer Doman
Cover of the book Fundamentals of Nanotransistors by Brian George Spencer Doman
Cover of the book Escape from Leipzig by Brian George Spencer Doman
Cover of the book Thermal Energy at the Nanoscale by Brian George Spencer Doman
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy