A generalization of the continuous Euler transformation and its application to numerical quadrature. (Q1405196)

The continuous Euler transformation was introduced by the author [ibid. 130, 259--270 (2001; Zbl 2002.09516)]. It is an analogue of the well-known Euler transform for series. In this paper the author presents new continuous transformations in an analogy of sequence transformations and shows that \textit{H. E. Salzer} and \textit{G. M. Kimbro's} transformation for sequences [Math. Comput. 15, 23--39 (1961; Zbl 0096.32204)] has a continuous analogue which accelerates convergence of an infinite integral with an algebraically decaying integrand. Some numerical examples are given.