Fredholm Integral Equation of the Second Kind

An Integral Equation of the form

$$\phi(x) = f(x)+\lambda\int_{-\infty}^\infty K(x,t)\phi(t)\,dt$$

$$\phi(x) = {1\over\sqrt{2\pi}} \int_{-\infty}^\infty {F(t)e^{-ixt}\,dt\over 1-\sqrt{2\pi}\,\lambda K(t)}.$$

See also Fredholm Integral Equation of the First Kind, Integral Equation, Neumann Series (Integral Equation), Volterra Integral Equation of the First Kind, Volterra Integral Equation of the Second Kind

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 865, 1985.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Fredholm Equations of the Second Kind.'' §18.1 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 782-785, 1992.