# Talk:Integral equation

*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.*--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

**How to Cite This Entry:**

Integral equation.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Integral_equation&oldid=30325