On the summability of random Fourier–Jacobi series

This article explores the summability of random Fourier-Jacobi seriesin various functions spaces, where q (,) i (y), , > -1 are the orthonormal Jacobi polynomials and bi are scalars.The random coefficients Bi() are the Fourier-Jacobi coefficients of a symmetric stable process Z(t, ) of index [1, 2].It is established that the random Fourier series in Jacobi polynomials is summable in means, Cesro means, Rogosinski means, etc., in the sense of probability if bi are the Fourier-Jacobi coefficients of a function f C (, )[-1,1] space, under different conditions on the Jacobi parameters , , and .Further, the Nrlund summability, generalized Nrlund summability and lower triangular summability of random Jacobi series associated with the symmetric stable process Z(t, ) of index one is established for functions belonging to the L 1,(,)[-1,1] space.It has been noted that the conditions on the Jacobi parameters for random series differ from that of the Fourier-Jacobi series.