Analytical method for calculating eigenvalues in the problem of nonstationary heat conduction of a spherical body

A method for investigating characteristic equations is proposed, and analytical formulas are obtained for determining the roots of the characteristic equation in the problem of nonstationary heat conduction of a spherical body. These formulas make it possible to determine any required number of roots with high accuracy, which is especially important when solving heat conduction problems at the initial moment of time. The proposed method can be used to study more complex characteristic equations arising in other heat transfer problems.