In this paper, we considered the non-uniformly distributed zeros on the unit circle, which are obtained by projecting vertically the zeros of the derivative of Legendre polynomial together with x=1 and x=-1 onto the unit circle. We prescribed the function on the above said nodes, while its second derivative at all nodes except at x=1 and x=-1 with suitable weight function and obtained the existence, explicit forms and establish a convergence theorem for such interpolatory polynomial. We call such interpolation as weighted Lacunary interpolation on the unit circle.
Bahadur, Swarnima and Bano, Sariya
(R1521) On Weighted Lacunary Interpolation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
1, Article 12.
Available at: https://digitalcommons.pvamu.edu/aam/vol17/iss1/12