Result: Upper bounds for the first zero of the Bessel function \(J_ \alpha(x)\).

Title:
Upper bounds for the first zero of the Bessel function \(J_ \alpha(x)\).
Authors:
Gatteschi, Luigi, Giordano, Carla
Publisher Information:
Accademia delle Scienze di Torino, Torino
Subject Terms:
Bessel and Airy functions, cylinder functions, \({}_0F_1\), Numerical approximation and evaluation of special functions
Document Type:
Academic journal Article
File Description:
application/xml
Access URL:
https://zbmath.org/1870366
Accession Number:
edsair.c2b0b933574d..81b53625b5d2b80917b8abebf0eee33f
Database:
OpenAIRE

Further Information

Summary: We present some new bounds for the first positive zero \(j_{\alpha,1}\) of the Bessel function \(J_\alpha(x)\), \(\alpha>-1\). The bounds are obtained by applying a Sturm-type comparison theorem to two differential equations satisfied by the ultraspherical polynomial \(P_n^{(\alpha, \alpha)}(x)\) and by the Bessel function \(J_\alpha(x)\), respectively. The new results are illustrated and compared with the previous ones.