Uniform convergence of basic Fourier-Bessel series on a q-linear grid

Area of Science:

• Mathematical Analysis
• Special Functions
• Fourier Analysis

Background:

• Fourier-Bessel series are essential tools in mathematical analysis.
• Understanding convergence properties is crucial for their application.
• Previous work has explored various orthogonal systems for series expansions.

Purpose of the Study:

• To investigate Fourier-Bessel series on a q-linear grid.
• To establish sufficient conditions for the uniform convergence of these series.
• To demonstrate the practical application of the convergence results.

Main Methods:

• Construction of complete q-orthogonal systems.
• Utilizing the third Jackson q-Bessel function.
• Derivation of sufficient conditions for uniform convergence.

Main Results:

• Sufficient conditions for uniform convergence of Fourier-Bessel series on a q-linear grid were obtained.
• The study provides a theoretical framework for analyzing these series.
• Convergence results were illustrated with specific examples.

Conclusions:

• The developed conditions provide valuable insights into the behavior of Fourier-Bessel series on q-linear grids.
• The findings contribute to the theory of special functions and Fourier analysis.
• The research validates the utility of q-orthogonal systems in convergence studies.