Carleman's equation
id:
carleman-s-equation-202-11408022
title:
Carleman's equation
text:
In mathematics, Carleman's equation is a Fredholm integral equation of the first kind with a logarithmic kernel. Its solution was first given by Torsten Carleman in 1922.
The equation is The solution for b − a ≠ 4 is If b − a = 4 then the equation is solvable only if the following condition is satisfied In this case the solution has the form where C is an arbitrary constant. For the special case f(t) = 1 (in which case it is necessary to have b − a ≠ 4), useful in some applications, we get
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https://en.wikipedia.org/wiki/Carleman%27s_equation
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date modified:
2017-05-31T14:42:40Z
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