Difference between revisions of "Delta cosh minus delta sinh"
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<strong>[[Delta cosh minus delta sinh|Theorem]]:</strong> The following formula holds: | <strong>[[Delta cosh minus delta sinh|Theorem]]:</strong> The following formula holds: | ||
$$\cosh^2_p - \sinh^2_p = e_{-\mu p^2},$$ | $$\cosh^2_p - \sinh^2_p = e_{-\mu p^2},$$ | ||
| − | where $\cosh_p$ denotes the [[Delta cosh|$\Delta$-$\cosh_p$]] function, $\sinh_p$ denotes the [[Delta sinh|$\Delta$-$\sinh_p$]] function, and $e_p$ denotes the [[Delta exponential|$\Delta$-$ | + | where $\cosh_p$ denotes the [[Delta cosh|$\Delta$-$\cosh_p$]] function, $\sinh_p$ denotes the [[Delta sinh|$\Delta$-$\sinh_p$]] function, and $e_p$ denotes the [[Delta exponential|$\Delta$-$e_p$]] function. |
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
</div> | </div> | ||
</div> | </div> | ||
Revision as of 18:09, 21 March 2015
Theorem: The following formula holds: $$\cosh^2_p - \sinh^2_p = e_{-\mu p^2},$$ where $\cosh_p$ denotes the $\Delta$-$\cosh_p$ function, $\sinh_p$ denotes the $\Delta$-$\sinh_p$ function, and $e_p$ denotes the $\Delta$-$e_p$ function.
Proof: █
