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Volumn 77, Issue 4, 2008, Pages

Method to calculate the moments of the membrane voltage in a model neuron driven by multiplicative filtered shot noise

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC POTENTIAL; MATHEMATICAL MODELS; PROBLEM SOLVING; SHOT NOISE; WHITE NOISE;

EID: 42449158079     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.041913     Document Type: Article
Times cited : (26)

References (26)
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    • The principal branch of the Lambert W function is the inverse function of y=x ex for x -1. If one extends the range of definition for the latter function to arguments smaller than minus one, the function is not monotonic anymore. Thus, one can divide the range of definition in two sets (x≤-1 and x -1), where different inverse functions are valid. Both inverse functions agree for x=-1. In our case, x=-b≤-1 and thus the principal branch of the Lambert W function is not the inverse function. Therefore, the trivial identity A=-b+b=0 is only fulfilled in the limit b→-1.
    • The principal branch of the Lambert W function is the inverse function of y=x ex for x -1. If one extends the range of definition for the latter function to arguments smaller than minus one, the function is not monotonic anymore. Thus, one can divide the range of definition in two sets (x≤-1 and x -1), where different inverse functions are valid. Both inverse functions agree for x=-1. In our case, x=-b≤-1 and thus the principal branch of the Lambert W function is not the inverse function. Therefore, the trivial identity A=-b+b=0 is only fulfilled in the limit b→-1.


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