
SIGMA 7 (2011), 022, 12 pages arXiv:0912.2135
http://dx.doi.org/10.3842/SIGMA.2011.022
Beyond the Gaussian
Kazuyuki Fujii
Department of Mathematical Sciences, Yokohama City University, Yokohama, 2360027 Japan
Received January 12, 2011, in final form February 28, 2011; Published online March 04, 2011
Abstract
In this paper we present a nonGaussian integral based on a
cubic polynomial, instead of a quadratic, and give a fundamental formula
in terms of its discriminant.
It gives a mathematical reinforcement to the recent result by Morozov
and Shakirov.
We also present some related results.
This is simply one modest step to go beyond the Gaussian
but it already reveals many obstacles
related with the big challenge of going further beyond the Gaussian.
Key words:
nonGaussian integral; renormalized integral; discriminant; cubic equation.
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