# Convergence of Fourier series in Jacobi polynomials in weighted Lebesgue space with variable exponent

### DOI: 10.31029/demr.8.4

The problem of basis property of the Jacobi polynomials system in the weighted Lebesgue space with variable exponent and is considered. It is shown that if and satisfies on some natural conditions then the orthonormal Jacobi polynomials system is a basis of as , .

Keywords: Basis property of the Jacobi polynomials, Fourier-Jacobi sums, convergence in the weighted Lebesgue space with variable exponent, Dini-Lipshits condition.

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