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<i>The text below has been removed from the page because it is based on a source which does not occur in either MathSciNet or Zentralblatt für Mathematik.</i>--[[User:Ulf Rehmann|Ulf Rehmann]] 19:40, 3 September 2013 (CEST)


===Integral equations solution in terms of power series===
In may cases if the Kernel of the integral equation is of the form K(xt) and the
[[Mellin transform]] of K(t) exists we can find the solution of the integral equation

\begin{equation} g(s)=s \int_{0}^{\infty}dtK(st)f(t) \qquad

 f(t)= \sum_{n=0}^{\infty}\frac{a_{n}}{M(n+1)}x^{n} \end{equation} 

with \begin{equation} g(s)= \sum_{n=0}^{\infty}a_{n} s^{-n}  \qquad M(n+1)=\int_{0}^{\infty}dtK(t)t^{n} \end{equation}

[9] Jose Javier Garcia Moreta "http://www.prespacetime.com/index.php/pst/issue/view/42 Borel Resummation & the Solution of Integral Equations