A new sequence of eigenfunctions is developed and studied in depth. These theta polynomials are derived from a recent analytic solution of the canonical Cauchy problem for parabolic equations, namely, the inverse heat conduction problem. By appealing to the methods of the operator calculus, it is possible to categorize the new functions as polynomials of binomial and Sheffer types. The connecti...

Temperature distributions recorded by thermocouples in a solid body (slab) subject to surface heating are used in a mathematical model of 2-D heat conduction. The corresponding Dirichlet problem for a holomorphic function (complex potential), involving temperature and heat stream function, is solved in a strip. The Zhukovskii function is reconstructed through singular integrals, involving an au...