# Kronecker Delta

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## Kronecker delta

[′krō·nek·ər ‚del·tə]
(mathematics)
The function or symbol δij dependent upon the subscripts i and j which are usually integers; its value is 1 if i = j and 0 if ij.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Kronecker Delta

a function δnm that is dependent on two integral arguments n and m and is defined by An example of the use of the Kronecker symbol is The Kronecker symbol was introduced by L. Kronecker in 1866.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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The number of separate terms in the expressions for the generalized Kronecker delta, if written only by using the standard Kronecker delta symbol, is given by the so-called double factorial (2n)!/(2"n!).
Lemma 3.3 Let [[alpha].sub.i] = [C.sub.i-1] + [[delta].sub.i,1] where [[delta].sub.i,1] denotes the Kronecker delta. Then the central binomial coefficient is given by the sum
where [R.sub.out] = R(x, [y.sub.obs], z), [R.sub.in] = R(x, -[y.sub.obs], z), [[delta].sub.wg] is the Kronecker delta, g = [perpendicular to], [parallel] and w = [perpendicular to], [parallel] represent the incident and scattered wave polarization, respectively, and
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes system (1)-(2) response to Kronecker delta [delta](k - [k.sub.0]) at time [k.sub.1], i.e.
Let [[delta].sub.i] (j) be the Kronecker delta function on S, that is for i, j [member] S
[[delta].sub.ij] is the Kronecker delta tensor and [eta] is the viscosity.
where [[delta].sub.k-j] is the Kronecker delta function given by
where the brackets <> denote the so-called projection, i.e., the inner product and where [delta] denotes the Kronecker delta. From these basis vectors, we define their tetrad components as
where the Kronecker delta guarantees the neutrality of the system.
with I = 1/2([[delta].sub.ik][[delta].sub.jl] + [[delta].sub.il][[delta].sub.jk]), where [delta] is the Kronecker delta. Finally, the continuum tangent elastoplastic tensor [a.sup.ep] is defined as

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