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As the title indicates, the book is designed with the goal of application front and center. That said, it is also important to note that the theoretical background is developed with full mathematical rigor. You can easily see this from the fact that whenever an infinite series is differentiated, its uniform convergence in the region of interest is always established beforehand. And this is just one example.
Now, given the fact that special functions is a vast subject, and the fact that the book is barely 300 pages long, it is obvious that the theoretical coverage, though rigorous, has to be reined in. By this I refer to the fact that most functions are developed from the point of view of series solutions to differential equations, while solution by contour integrals in the plane is basically absent. But then again, it doesn't matter how you develop the functions, the key is to know their properties and be able to apply them. The book will show you just how to do that. HIGHLY RECOMMENDED.
For a more broad-based theoretical coverage, I recommend Whittaker and Watson (but of course), and the book "Special Functions" by X. Z. Wang. These two books complement each other like lovers.
Now, given the fact that special functions is a vast subject, and the fact that the book is barely 300 pages long, it is obvious that the theoretical coverage, though rigorous, has to be reined in. By this I refer to the fact that most functions are developed from the point of view of series solutions to differential equations, while solution by contour integrals in the plane is basically absent. But then again, it doesn't matter how you develop the functions, the key is to know their properties and be able to apply them. The book will show you just how to do that. HIGHLY RECOMMENDED.
For a more broad-based theoretical coverage, I recommend Whittaker and Watson (but of course), and the book "Special Functions" by X. Z. Wang. These two books complement each other like lovers.
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