Difference between revisions of "Period of tanh"
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(Created page with "==Theorem== The following formula holds for all $k \in \mathbb{Z}$: $$\tanh(z+\pi i k)=\tanh(z),$$ where $\tanh$ denotes the hyperbolic tangent, $\pi$ denotes pi,...") |
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Period of cosh|next= | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Period of cosh|next=Pythagorean identity for sinh and cosh}}: $4.5.15$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 22:23, 21 October 2017
Theorem
The following formula holds for all $k \in \mathbb{Z}$: $$\tanh(z+\pi i k)=\tanh(z),$$ where $\tanh$ denotes the hyperbolic tangent, $\pi$ denotes pi, and $i$ denotes the imaginary number.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.15$
