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: | ||
| − | $$\sin( | + | $$\sin(az)=az{}_0F_1 \left(;\dfrac{3}{2};-\dfrac{(az)^2}{4} \right),$$ |
where $\sin$ denotes the [[sine]] and ${}_0F_1$ denotes the [[hypergeometric pFq]]. | where $\sin$ denotes the [[sine]] and ${}_0F_1$ denotes the [[hypergeometric pFq]]. | ||
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Revision as of 04:00, 19 August 2015
Theorem: The following formula holds: $$\sin(az)=az{}_0F_1 \left(;\dfrac{3}{2};-\dfrac{(az)^2}{4} \right),$$ where $\sin$ denotes the sine and ${}_0F_1$ denotes the hypergeometric pFq.
Proof: █
