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I am an undergrad student.We have a course on improper integrals of first and second kind along with beta and gamma function.I am looking for a suitable text that describes the problems and theory in detail.I have referred to S K Mapa,Real analysis but the book is not suitable for me.Can someone suggest any analysis text for improper integrals.

I am looking for the following subtopics:

$1.$ Improper integrals $\int_a^b f(x)dx$ with infinite discontinuity at $a$ and $\int_a^\infty f(x)dx$ in which range of integration is unbounded.

$2.$ Tests for improper integrals such as Comparison test,$\mu$-test etc.

$3.$ Beta gamma function and properties.

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Emanuel Fischer, Intermediate Real Analysis, Chapter XV, page 710. The matter about Gamma and Beta functions is discussed in page 726 - 735.

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  • $\begingroup$ the pdf is not available. $\endgroup$ Commented May 4, 2021 at 15:19
  • $\begingroup$ Hey, of course you don't expect that. But I believe that university library will have that, as I have stayed in three universities, there is the book. $\endgroup$ Commented May 4, 2021 at 15:21

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