Special functions in physics and engineering :a renewed approach with applications /

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"Version: 20241201"--Title page verso.Includes bibliographical references and index.1. Functions of complex variables -- 2. Boundary value problems -- 3. Riemann boundary value problem -- 4. Riemann boundary value problem with discontinuous coefficients and closed contours -- 5. Mechanical applications -- 6. Taylor and Laurent series and the residue theory -- 7. Singular points -- 8. Residues of regular functions at isolated singularities -- 9. Operator analysis -- 10. Multiplication and expansion theorem -- 11. Differential equations solution by the Laplace transform -- 12. Gamma function -- 13. Gamma function contour integral representation -- 14. Gamma function operator analysis -- 15. Beta function: first kind Euler integral -- 16. Asymptotic methods -- 17. Fuchsian equations--differential equations' singularities -- 18. Fuchsian class equation -- 19. Solution of the hypergeometric differential equation -- 20. Riemann differential equation transformed into the hypergeometric differential equation -- 21. Representation of elementary functions via hypergeometric functions -- 22. Hypergeometric-type integrals -- 23. Some properties of the hypergeometric functions -- 24. Lam?e generalized equation -- 25. Hypergeometric functions -- 26. Exponential integral and functions it generates -- 27. Laplace equation solution--hypergeometric and parabolic cylinder functions -- 28. Cylindrical functions of the first kind -- 29. Applications of cylindrical functions of the first kind -- 30. Cylindrical functions of the second kind -- 31. Cylindrical function of the third kind -- 32. Modified Bessel function -- 33. Thomson (Kelvin) functions and their generalizations -- 34. Contour integral representation of Bessel equation solution -- 35. Orthogonal cylindrical functions of the first kind -- 36. General theory of orthogonal polynomials -- 37. Jacobi polynomials -- 38. Ultraspherical (Gegenbauer) polynomials -- 39. Tschebycheff polynomials -- 40. Legendre polynomials -- 41. Spherical functions -- 42. Generalized Laguerre polynomial -- 43. Hermite polynomials -- 44. Elliptic functions -- 45. Lam?e and Mathieu functions.Full-text restricted to subscribers or individual document purchasers.A comprehensive-student-friendly and self-contained structured textbook aimed at stimulating students' interests and curiosity on special functions, organized in a logical and simple manner in order of complexity. The balance between theory and pertinent worked examples, which is an integral part of each chapter, reinforces the reader's understanding of the fundamental concepts. The analytical methods employed are written with mathematical rigor and clarity emphasizing a thorough knowledge of special functions with useful and helpful techniques for students pursuing graduate and undergraduate studies in mathematics, statistical and condensed matter physics, quantum mechanics, modern engineering and electronics. The comprehensive coverage of special functions and their applications in several areas of physics and engineering constitutes an unusually valuable reference and handbook.Advanced undergraduate and graduate students in physics, engineering and mathematics.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Lukong Cornelius Fai is professor of theoretical pysics at the Department of Physics, Faculty of Sciences, University of Dschang as well as visiting professor at the Department of Physics, Faculty of Science, University of Bamenda, both in Cameroon. He is Head of the Condensed Matter and Nanomaterials program at the Department of Physics, Faculty of Sciences, University of Dschang; he also heads the Condensed Matter, Electronics and Signal Processing as well as Mesoscopic and Multilayer Structures Laboratory at the Department of Physics, Faculty of Sciences, University of Dschang; and is Director of the College of Technology, University of Buea in Cameroon. He was formerly senior associate at the Abdus Salam International Centre for Theoretical Physics (ICTP), Italy. He holds a Master of Science degree in Physics and Mathematics (June 1991) as well as a Doctor of Science degree in Physics and Mathematics (February 1997) from the Faculty of Physics, Department of Theoretical Physics, Moldova State University. He has authored two hundred and nine scientific publications and six books.Title from PDF title page (viewed on January 17, 2025).

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: .,

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1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9780750361491

Classification

530.5

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Subject(s)

Mathematical physics.
MATHEMATICS / Applied.
Applied mathematics.
Engineering mathematics.
Functions, Special.

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Statement of Responsibility

Lukong Cornelius Fai.

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