According to a theorem in functional analysis, one of two examples of these functions has a nontrivial solution for every fixed, non-zero complex eigenvalue if a certain symmetric function is integer-valued.
One of these functions named after Niels Abel appears in the solution of a problem that asks for the curve in the vertical plane that starts at a given point and intersects the tau axis. There is an orthonormal set of eigenfunctions and eigenvalues that sums to one of these functions according to Mercer's Theorem. According to a theorem in functional analysis, one of two examples of these functions has a nontrivial solution for every fixed, non-zero complex eigenvalue if a certain symmetric function is integer-valued. In the Fredholm type of these equations, their associated (*) kernel is compact. Boundaries are set to unknown values in the Volterra type of these functions, which are often used to model radiosity and scattering problems since values of interest need to be calculated over a solid angle. For 10 points, name these equations in which variables of interest are expressed as a function of antiderivatives.
One of these functions named after Niels Abel appears in the solution of a problem that asks for the curve in the vertical plane that starts at a given point and intersects the tau axis.
integral equations [prompt on integro-differential equations; do not accept or prompt on integrable equations or differential equations]