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ON PARTIAL SUMS OF NORMALIZED q-BESSEL FUNCTIONS
Aktas, Ibrahim,Orhan, Halit Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.2
In the present investigation our main aim is to give lower bounds for the ratio of some normalized q-Bessel functions and their sequences of partial sums. Especially, we consider Jackson's second and third q-Bessel functions and we apply one normalization for each of them.
Bounds for radii of convexity of some q-Bessel functions
Ibrahim Aktas,Halit Orhan 대한수학회 2020 대한수학회보 Vol.57 No.2
In the present investigation, by applying two different normalizations of the Jackson's second and third $q$-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-P\'olya class of real entire functions plays an important role in this work.
BOUNDS FOR RADII OF CONVEXITY OF SOME q-BESSEL FUNCTIONS
Aktas, Ibrahim,Orhan, Halit Korean Mathematical Society 2020 대한수학회보 Vol.57 No.2
In the present investigation, by applying two different normalizations of the Jackson's second and third q-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-Pólya class of real entire functions plays an important role in this work.