THEOREM 4.3.3 Tanh z, coth z. sech z, and each z are analytic func tions of z, except for those values of z excluded by Definition 4.3.2. Moreover, (tanh z) sech²z dz d dz d dz (coth z)=-csch²z (sech z)=- sech z tanh z + where, in all cases, n = 0, 1, 2, . (z+nwi). (esch z)=-csch z coth z (z nai). (4.3.7)

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