Halving identity for tangent (3)

From specialfunctionswiki
Revision as of 22:50, 21 October 2017 by Tom (talk | contribs) (Created page with "==Theorem== The following formula holds: $$\tanh \left( \dfrac{z}{2} \right) = \dfrac{\sinh(z)}{\cosh(z)+1},$$ where $\tanh$ denotes hyperbolic tangent, $\sinh$ denot...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Theorem

The following formula holds: $$\tanh \left( \dfrac{z}{2} \right) = \dfrac{\sinh(z)}{\cosh(z)+1},$$ where $\tanh$ denotes hyperbolic tangent, $\sinh$ denotes hyperbolic sine, and $\cosh$ denotes hyperbolic cosine.

Proof

References