Z coth(z) = 2z/(e^(2z)-1) + z
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Theorem
The following formula holds for $|z|<\pi$: $$z \mathrm{coth}(z) = z+\dfrac{2z}{e^{2z}-1},$$ where $\mathrm{coth} denotes hyperbolic cotangent and $e^{2z}$ denotes the exponential.
Proof
References
- 1953: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $\S 1.20 (1)$
