Ordering relations between the zeros of miscellaneous bessel functions

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Abstract
A method applied in previous work [l,10,11] to the study of the zeros of the ordinary Bessel function JĪµ (z) is here extended and also applied to the zeros of the function , is the derivative of JĪ½ (z). It is proved that in the case where Ī½ is real and Ī½>āˆ’1, the zeros of F Ī½(z) are the same with the zeros of the function , where T (x), in the case of real positive zeros, meromorphic with poles the positive zeros of JĪ½(z). Moreover the function T(x) is real for x real and increases as x increases in each of the intervals . This result unifies generalizes and improves, many known results for the zeros of the interesting function .
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