Difference between revisions of "Relationship between sine and hypergeometric 0F1"
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<strong>[[Relationship between sine and hypergeometric 0F1|Theorem]]:</strong> The following formula holds: | <strong>[[Relationship between sine and hypergeometric 0F1|Theorem]]:</strong> The following formula holds: | ||
$$\sin(az)=az{}_0F_1 \left(;\dfrac{3}{2};-\dfrac{(az)^2}{4} \right),$$ | $$\sin(az)=az{}_0F_1 \left(;\dfrac{3}{2};-\dfrac{(az)^2}{4} \right),$$ | ||
| − | where $\sin$ denotes the [[sine]] and ${}_0F_1$ denotes the [[hypergeometric pFq]]. | + | where $\sin$ denotes the [[sine]] function and ${}_0F_1$ denotes the [[hypergeometric pFq]]. |
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
</div> | </div> | ||
</div> | </div> | ||
Revision as of 04:00, 19 August 2015
Theorem: The following formula holds: $$\sin(az)=az{}_0F_1 \left(;\dfrac{3}{2};-\dfrac{(az)^2}{4} \right),$$ where $\sin$ denotes the sine function and ${}_0F_1$ denotes the hypergeometric pFq.
Proof: █
