Abstract
In this work two-phase Stefan problem for the cylindrical heat equation is considered.One of the phase turns to zero at an initial time.In this case, it is difficult to solve it by radial heat polynomials because the equations are singular.The solution is represented in linear combination series of special functions, the Laguerre polynomial and confluent hypergeometric function.The free boundary is known.The undetermined coefficients of the heat in two phases and the heat flux are found.The convergence of special functions series is proved.