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Insights A Novel Technique of Calculating Unit Hypercube Integrals
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The article presents a novel technique for evaluating unit hypercube integrals, beginning with a theorem on Dirichlet integrals. It introduces a sequence of nested sets that converge point-wise to a unit hypercube, integrating these concepts using the Dominated Convergence Theorem. The technique aims to provide a systematic approach to integration, enhancing understanding of Dirichlet integrals, which are linked to Gamma functions. Additionally, the article references an expanded insight piece that explores fractional integral representations of special functions. The discussion culminates with the completion of solutions to related exercises for further learning.
Hello!
I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem.
Given:
##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0##
##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1##
##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0##
I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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