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1. the act or process of determining a sum; addition
2. the result of such an act or process
3. US law the concluding statements made by opposing counsel in a case before a court
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



in physiology, the cumulative effect of several stimuli following one another in rapid succession (temporal summation) or occurring simultaneously (spatial summation) and arising in such excitable structures as receptors, neurons, and muscles.

Summation was first described in 1868 by I. M. Sechenov, who observed that under certain conditions of rhythmic stimulation there was a delay in the appearance and subsequent intensification of reflexes. Temporal summation occurs in the intervals between stimuli. These intervals are limited by the period of subthreshold or trace shifts in membrane potential toward depolarization, with development of excitation, or toward hyper-polarization, with development of inhibition. Temporal summation ensures that the duration of the reaction will be sufficient and that it can be maintained by the circular relationship between the neurons.

Spatial summation changes continuously and is manifested by the simultaneous excitation or inhibition of many neurons in different parts of the brain as well as of numerous synapses in a single neuron. Summation helps to intensify individual reactions and to coordinate the body’s reactions. In muscles, spatial summation intensifies contractions by increasing the number of excited motor units, that is, groups of fibers innervated by a single neuron. Temporal summation in muscles induces tetanus by uniting successive individual contractions.


The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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Summation is also your chance to point out inconsistencies in the defense case.
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Proof: Letting [S.sub.N] be the value of the summation, by induction it is seen that the equation for recursion, at stage M, is given by:
The mock theta functions were there and my simple summation identity in (9) was a tool, to give generating functions for the partial mock theta functions.