Method for m-Dimensional Integration


By generalizing the methods for double and triple integration, I have prepared a set of rules for integration over m variables. This technique may find applications in analyzing high-dimensional networks of spiking neurons, in quantum mechanics, and elsewhere.

  • Linearity holds for m-dimensional integrals, allowing the rules for integrating various functions to be combined.
  • The rules for m-dimensional integrals will hold for infinite-dimensional integrals.
  • Below, rules for computing m-dimensional polynomial functions, product functions, and sums of exponential functions are given. 

m-dimensional integration rules

  • Some special cases of the above rules are given next to simplify calculations under these particular conditions.

m-dimensional integration special cases

 

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