Mathematical Aspects of Krätzel Integral and Krätzel Transform

Abstract

A real scalar variable integral is known in the literature by different names in different disciplines. It is basically a Bessel integral called specifically Krätzel integral. An integral transform with this Krätzel function as kernel is known as Krätzel transform. This article examines some mathematical properties of Krätzel integral, its connection to Mellin convolutions and statistical distributions, its computable representations, and its extensions to multivariate and matrix-variate cases, in both the real and complex domains. An extension in the pathway family of functions is also explored.

Keywords

• Mellin convolutions
• Krätzel integrals
• reaction-rate probability integral
• continuous mixtures
• Bayesian structures
• fractional integrals