On the Convergence of Jacobi Series at the Poles

The most urgent need in information Technology is data compilation for different purposes in varying ways. Convergence of Jacobi series is used for replacement of discontinuous signals by its approximated absolutely continuous signals for data manipulation in computers. Here in this paper a Banach space X of signals which are p-power Lebesgue integrable with weight on [-1,1] is considered. Some of subspaces of X have been recognized by the convergence behavior of Fourier-Jacobi expansions associated with the signals. These results are applied to signal processing with wavelets related to useful concept in Science and Engineering disciplines.