TY  - BOOK
AU  - Fai,Lukong Cornelius
ED  - Institute of Physics (Great Britain),
TI  - Special functions in physics and engineering: a renewed approach with applications 
T2  - [IOP release $release]
SN  - 9780750361491
AV  - QC20.7.F87 F357 2024eb
PY  - 2024///]
CY  - Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK)
PB  - IOP Publishing
KW  - Functions, Special
KW  - Mathematical physics
KW  - Engineering mathematics
KW  - Applied mathematics
KW  - bicssc
KW  - MATHEMATICS / Applied
KW  - bisacsh
N1  - "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; Advanced undergraduate and graduate students in physics, engineering and mathematics; Also available in print
N2  - 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
UR  - https://iopscience.iop.org/book/mono/978-0-7503-6149-1
ER  -