On the zeros ofJν″′(x)
Chrysi G. Kokologiannaki, Eugenia N. Petropoulou · Integral Transforms and Special Functions · 2012
The zeros of J″′ν(x) are studied by using classical analysis and the properties of J ν(x). It is proved that J″′ν(x) has infinite positive zeros and between two consecutive positive zeros of J ν(x), there exist at least one zero of J ν″′(x) for ν>1. Moreover, several theorems are given regarding their location depending on the values of ν. Also, alternative proofs are given regarding the monotonicity of the positive zeros of J″′ν(x) for ν>(1+√5)/2 and ν>1.