Dirac delta function

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Dirac delta function

[di′rak ′del·tə ‚fəŋk·shən]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Putting [[delta].sub.n](x) = n[rho](nx) for n = 1, 2,..., it follows that {[[delta].sub.n](x)} is a regular sequence of infinitely differentiable functions converging to the Dirac delta-function [delta](x).
It is easily forgotten that the individual of species i at location x cannot itself be a member of its neighborhood; the term [[delta].sub.ij] X [[delta].sub.x](x') comprising the Kronecker delta [[delta].sub.ij] multiplied by the Dirac delta-function [[delta].sub.x](x') subtracts this individual from the integrated expression (the Kronecker delta [[delta].sub.ij] takes value 1 when i = j, and 0 otherwise).