We consider the modifications of the monic Hermite and Gegenbauer polynomials via the addition of one point mass at the origin. Some properties of the resulting polynomials are studied: three-term recurrence relation,...We consider the modifications of the monic Hermite and Gegenbauer polynomials via the addition of one point mass at the origin. Some properties of the resulting polynomials are studied: three-term recurrence relation, differential equation, ratio asymptotics, hypergeometric representation as well as, for largen, the behaviour of their zeros.展开更多
文摘We consider the modifications of the monic Hermite and Gegenbauer polynomials via the addition of one point mass at the origin. Some properties of the resulting polynomials are studied: three-term recurrence relation, differential equation, ratio asymptotics, hypergeometric representation as well as, for largen, the behaviour of their zeros.
