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Does anybody know the history of how Peter Gustav Lejeune Dirichlet came up with the “nowhere continuous” Dirichlet function?
So I am writing a research paper on the properties of the Dirichlet function (the function with 1 if x is rational and 0 if x is irrational), and I wanted to include some historical background on how ...
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Dirichlet integral's history
I was calculating the so-called Dirichlet Integral,
$$\displaystyle \int_{0}^{\infty}\frac{\sin x}{x} \text{d} x$$
and then I wondered about his name and history:
Why it has the name of Dirichlet?
...
