Special functions for optical science and engineering

This tutorial text is for those who use special functions in their work or study but are not mathematicians. Traditionally, special functions arise as solutions to certain linear second-order differential equations with variable coefficients--equations having applications in physics, chemistry, engi...

Ausführliche Beschreibung

Gespeichert in:
Hauptverfasser:
Lakshminarayanan, Vasudevan, Varadharajan, L. Srinivasa
Format:
Elektronisch E-Book
Sprache:
Englisch
Veröffentlicht:
2015
Zusammenfassung:
This tutorial text is for those who use special functions in their work or study but are not mathematicians. Traditionally, special functions arise as solutions to certain linear second-order differential equations with variable coefficients--equations having applications in physics, chemistry, engineering, etc. This book introduces these differential equations, their solutions, and their applications in optical science and engineering. In addition to the common special functions, some less common functions are included. Also covered are Zernike polynomials, which are widely used in characterizing the quality of any imaging system, as well as certain integral transforms not usually covered in elementary texts. The book is liberally illustrated, and almost every chapter includes a set of Python 3.x codes that illustrate the use of these functions. Readers with a modest introduction to programming concepts will be able to modify these sample codes as needed
Umfang:
1 online resource (xix, 389 pages)
Anmerkungen:
"SPIE Digital Library."--Website. - Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader
Preface -- Acknowledgment -- 1. Introduction -- 2. Gamma, beta, and error functions -- 3. Other integral functions -- 4. Airy functions -- 5. Bessel functions -- 6. Chebyshev polynomials -- 7. Hermite polynomials -- 8. Gegenbauer, Jacobi, and orthogonal polynomials -- 9. Laguerre polynomials -- 10. Legendre functions -- 11. Mathieu functions -- 12. Hypergeometric functions -- 13. Integral transforms -- 14. Zernike polynomials -- Appendix A. Series solution of differential equations -- Appendix B. Python basics -- Appendix C. Additional reading -- Postscript -- References -- Index
Schriftenreihe:
Tutorial texts in optical engineering
ISBN:
9781628416688
9781628418873
Schlagworte:
Optical engineering / Mathematics
Links: