Product formula for the generalized q-Bessel function

Abstract

The aim of this paper is to establish a product formula for the generalized q-Bessel function which is a generalization of the known q-Bessel functions of kind 1,2,3, the modified q-Bessel functions of kind 1,2,3, and the new q-analogy of the modified Bessel function presented and studied by Mansour and Al-Shomarani. As an application of the product formula we derive Turán-type inequality for the modified q-Bessel function of third kind.

Keywords:

• q-Bessel functions
• modified q-Bessel functions
• product formula
• Turán type inequalities

AMS Subject Classifications:

• 33D15
• 33D45
• 33C10
• 39B62

Notes

No potential conflict of interest was reported by the authors.