Function cosech

The other hyperbolic functions, tanh, cosech, sech andcoth, defined in terms sinh and cosh, are the hyperbolic analogues of the functions tan, cosec, sec and cotan, and are defined as follows ... 

The cosech function are expanded as a power series in kT. Inversion of the Laplace transform then gives a series solution for the density of states, whose first term is the same as the Marcus-Rice correction, Eq. (85), and whose subsequent terms are corrections containing smaller powers of -f- E. Ultimately the expansion of the partition function gives terms with negative powers of kT, which invert to delta functions and derivatives of delta functions, but truncating the series before this happens gives good smooth approximations to the density of states. 

The remaining four hyperbolic functions, analogous to the remaining four trigonometrical functions, are tanh u, cosech u, sech u and coth u. Values for each of these functions may be deduced from their relations with sinh u and cosh u. Thus,... 

The Z- and Y-parameter methods are stable for 0 oo since it is based on the convergence functions coth(0) and cosech(0). Thus, the method is suitable for transient analysis. However, it should not be used for analyzing low-frequency phenomena since cosech(0) becomes infinite for 0 -> 0, that is, co 0. 

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