Mathematical Aspects of Krätzel Integral and Krätzel Transform
Abstract
:1. Introduction
1.1. Krätzel Integral
1.2. Evaluation of the Integral in Equation (2)
1.3. Computable Series form for Equation (2)
1.4. G-function in the Simple Poles Case
1.5. Poles of Order Two,
2. Krätzel Integral from Mellin Convolution
3. Krätzel Integral as the Density of a Product
4. Krätzel Integral and Bayesian Structures
5. Pathway Extension of Krätzel Integral
Connection to Kobayashi Integrals
6. Multivariate Extensions of Krätzel Integrals
Connections to Fractional Integrals
7. Krätzel Integral in the Real Matrix-variate Case
8. Krätzel Integral in the Complex Matrix-variate Case
9. Extension to Rectangular Matrix-variate Case
9.1. Multivariate Situation
9.2. Evaluation of the Normalizing Constant
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Mathai, A.M.; Haubold, H.J. Mathematical Aspects of Krätzel Integral and Krätzel Transform. Mathematics 2020, 8, 526. https://doi.org/10.3390/math8040526
Mathai AM, Haubold HJ. Mathematical Aspects of Krätzel Integral and Krätzel Transform. Mathematics. 2020; 8(4):526. https://doi.org/10.3390/math8040526
Chicago/Turabian StyleMathai, Arak M., and Hans J. Haubold. 2020. "Mathematical Aspects of Krätzel Integral and Krätzel Transform" Mathematics 8, no. 4: 526. https://doi.org/10.3390/math8040526
APA StyleMathai, A. M., & Haubold, H. J. (2020). Mathematical Aspects of Krätzel Integral and Krätzel Transform. Mathematics, 8(4), 526. https://doi.org/10.3390/math8040526