Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 3 1 2015 03 02 Moment Problem and Inverse Cauchy Problems for Heat Equation 33 36 EN O. Yaremko N. Yaremko Penza State University, Penza, Russia T. Eliseeva TJANT2015318 10.12691/tjant-3-1-8 2015 01 29 2015 02 22 2015 03 02 The solution of Hamburger and Stieltjes moment problem can be thought of as the solution of a certain inverse Cauchy problem. The solution of the inverse Cauchy problem for heat equation is founded in the form of Hermite polynomial series. The author reveals, the formulas obtained by him for the solution of inverse Cauchy problem have a symmetry with respect to the formulas for corresponding direct Cauchy problem. Obtained formulas for solution of the inverse problems can serve as a basis for the solution of the moment problem.