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Summation, which includes both spatial summation and temporal summation, is the process that determines whether or not an action potential will be generated by the combined effects of excitatory and inhibitory signals, both from multiple simultaneous inputs (spatial summation), and from repeated inputs (temporal summation).
In either case, the value at x = 0 is defined to be the limiting value := = for all real a ≠ 0 (the limit can be proven using the squeeze theorem). The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of π ).
An m-1-term, σ-approximated summation for a series of period T can be written as follows: = + = () [ + ()], in terms of the normalized sinc function: = . and are the typical Fourier Series coefficients, and p, a non negative parameter, determines the amount of smoothening applied, where higher values of p further reduce the ...
7.2 Sum of reciprocal of factorials. 7.3 Trigonometry and ... The first few values are:
When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β. Ptolemy's theorem is important in the history of trigonometric identities, as it is how results equivalent to the sum and difference formulas ...
According to temporal summation one would expect the inhibitory and excitatory currents to be summed linearly to describe the resulting current entering the cell. However, when inhibitory and excitatory currents are on the soma of the cell, the inhibitory current causes the cell resistance to change (making the cell "leakier"), thereby ...
The sign of the square root needs to be chosen properly—note that if 2 π is added to θ, the quantities inside the square roots are unchanged, but the left-hand-sides of the equations change sign. Therefore, the correct sign to use depends on the value of θ. For the tan function, the equation is:
In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation , named after Niels Henrik Abel who introduced it in 1826.