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Generalized Krätzel integral and associated statistical densities. (English) Zbl 1256.33010

Summary: Krätzel integral is one of the integrals appearing in applied analysis, engineering, physics and other areas. There is an integral transform associated with this basic integral, known as Krätzel transform. This transform is given generalization in the form of P-transform. This integral is also connected with various quantities in different disciplines such as inverse Gaussian density in statistical analysis, Bessel functions, Mellin convolution, etc. Various generalizations to the basic Krätzel integral, and the associated statistical densities, are given in the present paper. For each generalization, its connections to various quantities in different disciplines are pointed out. The generalizations cover a vast number of basic integrals in different disciplines.

MSC:

33E20 Other functions defined by series and integrals
44A20 Integral transforms of special functions
60E05 Probability distributions: general theory
62E15 Exact distribution theory in statistics
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