A differential equation for any positive zero of the function is found, where is the Bessel function of the first kind of is the derivative of and , are real numbers. It is proven that:
(i) The function decreases with in the case , and the function decreases with in the case .
(ii) The zeros of the function increase with in the case and with in the case . The first result leads to a number of lower and upper bounds for the zeros of the function which complete and improve previously known bounds The second result improves a well-known result.
Cite this article
E.K. Ifantis, P.D. Siafarikas, A Differential Equation for the Positive Zeros of the Function . Z. Anal. Anwend. 7 (1988), no. 2, pp. 185–192DOI 10.4171/ZAA/295