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I need to compute the following integral. $$ \int_0^a e^{-bx}\sqrt{4(a-x)}K_1(\sqrt{4(a-x))}dx\,. $$ where $$ a>0$$ and $b$ can be greater than zero or less than zero but it is not a complex number.

Any help will be much appreciated. Thanks in advance.

BR

Frank

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  • $\begingroup$ It will be of great help if somebody could point me to some reference where i can find similar kind of problems. Thanks $\endgroup$
    – Frank Moses
    Commented Dec 22, 2015 at 6:05
  • $\begingroup$ there might well be a closed form solution in certain limits of $a,b$ (would that be enough for you?), but not a general solution for any $a,b$. $\endgroup$
    – Carlo Beenakker
    Commented Dec 22, 2015 at 8:29
  • $\begingroup$ Thanks Carlo Beenakker for your interest. Yes that will be excellent. I will be happy to see such a solution. $\endgroup$
    – Frank Moses
    Commented Dec 23, 2015 at 0:46

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