Difference between revisions of "Halving identity for tangent (3)"
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(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...") |
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Halving identity for tangent (2)|next=Doubling identity for sinh}}: $4.5.30$ | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Halving identity for tangent (2)|next=Doubling identity for sinh (1)}}: $4.5.30$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 22:51, 21 October 2017
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
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.30$
