ABSTRACT

Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems.
The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included.
The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations.

chapter 1|42 pages

Preliminaries

chapter 2|29 pages

Special Functions

chapter 3|26 pages

Generalized Functions

chapter 4|15 pages

Function Transformations

chapter 5|32 pages

The Laplace Transform

chapter 6|15 pages

The Two-Sided Laplace Transform

chapter 7|11 pages

The Borel Transform

chapter 8|15 pages

The Stieltjes Transform

chapter 9|9 pages

The Lambert Transform

chapter 10|14 pages

The Mellin Transform

chapter 11|6 pages

Finite Mellin-Type Transforms

chapter 12|43 pages

The Fourier Transform

chapter 13|7 pages

The Hartley Transform

chapter 14|18 pages

The Hilbert Transform

chapter 15|10 pages

The Boas Transform

chapter 16|8 pages

The Mittag-Leffler Transform

chapter 17|15 pages

The Convolution Transform

chapter 18|12 pages

The Weierstrass Transform

chapter 19|8 pages

The Abel Transform

chapter 21|18 pages

The Hankel and Hankel-Type Transforms

chapter 22|8 pages

The Hardy Transform

chapter 23|8 pages

The K (Meijer) Transform

chapter 24|9 pages

The Kontorovich-Lebedev Transform

chapter 25|12 pages

The Mehler-Fock Transform

chapter 26|21 pages

The Sturm-Liouville-Type Transforms

chapter 27|11 pages

Miscellaneous Transforms

chapter 28|11 pages

The Bargmann Transform

chapter 29|18 pages

The Zak Transform

chapter 30|15 pages

The Gabor Transform

chapter 32|25 pages

The Wavelet Transform

chapter 33|23 pages

The Radon Transform

chapter 34|15 pages

Sequence Transformations