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In the present paper, we introduce the probability density functions involving non-zero zeros of the Bessel and Legendre functions. Then, we evaluate the distributions of the characteristic functions defined by these probability density functions and again obtain their related functions and polynomials. Finally, we prove the infinite divisibility of these probability density functions.

ON THE DISTRIBUTIONS OF THE DENSITIES INVOLVING NON-ZERO ZEROS OF BESSEL AND LEGENDRE FUNCTIONS AND THEIR INFINITE DIVISIBILITY