Representation of holomorphic functions by schlömilch’s series

✍ Scribed by Rusev, Peter

• Book ID: 120161139
• Publisher: SP Versita
• Year: 2013
• Tongue: English
• Weight: 131 KB
• Volume: 16
• Category: Article
• ISSN: 1311-0454
• DOI: 10.2478/s13540-013-0026-7

✦ Synopsis

Abstract
A necessary and sufficient condition is given for holomorphic functions to be represented by series of the kind $\sum\limits_{n = 0}^\infty {a_n J_0 (nz),z,a_n \in \mathbb{C},} $ where J 0(z) is the Bessel function of first kind with zero index. To derive the result, we use an Erdélyi-Kober operator of fractional order.