In this paper we have found that if a Kenmotsu manifold with a Killing vector field satisfies gradient Ricci soliton equation then the smooth function is either constant or is orthogonal to the Killing vector field.

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Abstract. Filippi [1] has proposed a quadrature scheme for any function f(x) in [-1, 1], based on expanding the integrand in a series of Chebyshev polynomials of the second kind. In this paper the error associated with this quadrature method when applied to analytic functions has been investigated in detail.

An attempt has been made to obtain error estimates in the approximation of a function using a series of Chebyshev polynomials of the second kind.Introduction. The desirability of obtaining expansions in Chebyshev polynomials of the first kind has been widely discussed in the literature. But the expansions in Chebyshev polynomials of the second kind are sometimes also used in problems of approximate quadrature because they offer the best approximation

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