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Can you recommend a good book (with theoretical results with proofs, and with plenty of solved problems and examples) on the topics of improper integrals, (improper) integrals with parameters, special functions (Beta, Gamma, ...)?

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    $\begingroup$ This thread may help. $\endgroup$ – Raymond Manzoni Apr 27 '14 at 21:24
  • $\begingroup$ I think I remember liking this book "An introduction to the theory of functions of a complex variable" by Copson, when I did a course on complex analysis last semester. He seems to do a good bit and I couldn't get through nearly half of it. It seems to be available here to read online: archive.org/details/TheoryOfTheFunctionsOfAComplexVariable $\endgroup$ – snulty May 7 '14 at 23:56
  • $\begingroup$ He does do a bit on special functions, gamma, beta, hypergeometric. Plus there's a search bar. It's from something like 1901 I think I read... Meant to be pretty decent though $\endgroup$ – snulty May 8 '14 at 0:04
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    $\begingroup$ an exercise book with solutions, amazon.com/Problems-Mathematical-Analysis-Student-Library/dp/… $\endgroup$ – OBDA May 8 '14 at 10:29
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You may have a look at the affordable and accessible Schaum's Outline of Advanced Calculus. Not too much advanced :)

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I like Hildebrand's 'Advanced Calculus for Applications'. It has many applications of special functions for differential equations and shows how to use them to solve problems.

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