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(P, Q)-Extended Bessel and Modified Bessel Functions of the First Kind
Results in Mathematics, 2017Inspired by certain recent extensions of the Euler's beta, Gauss hypergeometric and confluent hypergeometric functions [1], we introduce (p, q)- extended Bessel function J_{; ; ; \nu, p, q}; ; ; , the (p, q)- extended modified Bessel function I_{; ; ; ; \nu, p, q}; ; ; ; of the first kind of order \nu by making use two additional parameters in the ...
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On Zeros of the Modified Bessel Function of the Second Kind
Computational Mathematics and Mathematical Physics, 2020The zeros \(\nu_n\) of the modified Bessel function \(K_{i\nu}(x)\) at \textit{fixed} argument \(x>0\) are shown to be countably infinite and simple. By a suitable transformation of the differential equation satisfied by \(K_{i\nu}(x)\) into a one-dimensional Schrodinger equation with an exponential potential, the equation is expressed as a boundary ...
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