Abstract: Some applications of the Gegenbauer polynomials in physical problems are presented. The problems

discussed include heat conduction problem and Schrdinger equation in a spherical clove domain，and the effect of

an Aharonov-Bohm vector potential on the energy levels of bound states in a central potential.

Key words: Gegenbauer polynomials, equation of heat conduction, Schrdinger equation, Aharonov -Bohm effect, spherical clove domain