Abstract
We find sufficient conditions for the basisness of the system (\(\sqrt {x\rho k} {J_v}\left( {x\rho k} \right):k \in N\)) in the space L2(0; 1) and establish a relationship between the approximation properties of this system and the properties of the system (τν+1/2E1/2(−τ2ρk2; μ): k ∈ N), where Jν is the Bessel function of the first kind of index ν and Eρ(z; μ) is the Mittag-Leffler-type function.
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