Zeros of some special entire functions

Abstract

The real and complex zeros of some special entire functions such as Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, Pólya and Runckel. The obtained results extend the known theorem of Hurwitz on exact number of nonreal zeros of Bessel functions of the first kind. Moreover, results on zeros of derivatives of Bessel functions and cross-product of Bessel functions are also given, which are related to some recent open problems.

11 pages

References in corpus (3)

• Zeros of Bessel function derivatives
• Products of Bessel and modified Bessel functions
• Multiplier sequences, classes of generalized Bessel functions and open problems

Cited by in corpus (6)

• Products of Bessel and modified Bessel functions
• When does a hypergeometric function ${}_p{F}_q$ belong to the Laguerre--Pólya class $L{P}^{+}$?
• Some properties of the free stable distributions
• Riemann, Thorin, van Dantzig Pairs, Wald Couples and Hadamard Factorisation
• On the critical points of entire functions
• Geometric and monotonic properties of hyper-Bessel functions