A Bessel function inequality connected with stability of least square smoothing, II

Abstract

1. Present Results. In accordance with customary notation, /"(?) denotes the Bessel function of the first kind and order v, j v k its kth positive zero andy v 0 = 0.The object of this note is to prove that < 2 for all v^lThis inequality arose [7] in a problem of numerical analysis and was proved subsequently First we demonstrate that fjp.l fjp.lk+1 rjp.2k+tfor all p > i and k = 1,2, Proof of (3).In [1, p. 63 (3.5), p. 70 (ii)] it has been shown thatAdding M o to both sides and rearranging gives Remark. Up = \, the two sides of (3) become equal.https://www.cambridge.org/core/terms. https://doi