Geodesic
On mean convergence of Fourier--Jacobi series
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 3, pp. 43-59

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The conditions on coefficients for mean convergence of Fourier–Jacobi series are obtained. The asymptotic formulae for the best approximation in Lebesgue spaces are derived and an asymptotic equality for Valee–Poussin sums is obtained. Some properties of generalized shift function are also studied. 
@article{VMJ_2016_18_3_a5,
     author = {E. J. Ibrahimov},
     title = {On mean convergence of {Fourier--Jacobi} series},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {43--59},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a5/}
}
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E. J. Ibrahimov. On mean convergence of Fourier--Jacobi series. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 3, pp. 43-59. http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a5/