Zusammenhang zwischen einer Integrodifferentialgleichung und einer Funktionalgleichung (Q580632)

The integro-differential equation \[ f(t)+\lambda \int^{\infty}_{0}J_ n(2\sqrt{tx})(t/x)^{n/2}f^{(k)}(x)dx=h(t) \] is shown to be reduced by means of the Laplace transform to a functional equation which is easily solvable. An alternative theorem can then be formulated and proved, and the general form of the solutions is finally attained.