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Question:

Find the closed form of

$$I(x,y)=\int_{0}^{1}t^{-1/2}\left(1-\dfrac{t}{1+4y}\right)^{-1/2-ix}dt$$

where $i^2=-1$

I have used Wolfram Alpha but it can't help me out. How to find it?

Thank you

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china math110 also said that he can't comment. Here is the proof: How find all positive real $\beta$ such A finite number of $\left|\frac{p}{q}-\sqrt{2}\right|<\frac{\beta}{q^2}$

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1 Answers1

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If your x and y are independent of t, then the answer is simply an incomplete beta function.

Lucian
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