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Exchange the order of integral and summation

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Hey guys:

I am wondering is there any coding which could make exchange of order of integral and summation automatically. Please check the table in my nb file.

I met a lot of integral of Hypergeometric series, which is an infinite summation of power series (You may safely assume convergence here). As Mathematica could calculate hypergeometric function for any values, I believe if we do an exchange of order first, it is possible to have the numerical results. Expecting any ways to see the numerical results of the table in the nb file.

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POSTED BY: 喆昊 张
Answer
7 days ago

I would first use rational numbers such as 1/2 instead of floating point numbers such as 0.5. Then you can use Series:

Series[g[t], {t, 0, 5}]
POSTED BY: Gianluca Gorni
Answer
6 days ago

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