About a Formula for Calculating the Zeros of Analytic Functions

Abstract The problem of finding the zeros of a pair of functions, one analytic in a Jordan domain and the other in its complement, is considered. An integral representation is constructed for a polynomial having the same zeros (counting multiplicities) as these two functions. To derive this representation, we use the Gakhov–Muskhelishvili formulas for the solution of the Riemann linear conjugation problem. We present examples where the zeros of entire functions that arise when solving two problems in mathematical physics are calculated.