Thomas Bothner

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20122021

most citedAsymptotics of a Fredholm determinant involving the second Painlevé transcendent

3 citations · 8 across the 6 of their papers we have counts for

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math.CA2018

Rational Solutions of the Painlevé-III Equation: Large Parameter Asymptotics

Thomas Bothner, Peter D. Miller

The Painlevé-III equation with parameters $Θ_{0} = n + m$ and $Θ_{\infty} = m - n + 1$ has a unique rational solution $u (x) = u_{n} (x; m)$ with $u_{n} (\infty; m) = 1$ whenever $n \in Z$ . Using a Ri…

math.CA2018★ 2 cited

Rational Solutions of the Painlevé-III Equation

Thomas Bothner, Peter D. Miller, Yue Sheng

All of the six Painlevé equations except the first have families of rational solutions, which are frequently important in applications. The third Painlevé equation in generic form…