Difference between revisions of "Relationship between sine and hypergeometric 0F1"
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| − | + | ==Theorem== | |
| − | + | 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]] function and ${}_0F_1$ denotes the [[hypergeometric pFq]]. | where $\sin$ denotes the [[sine]] function and ${}_0F_1$ denotes the [[hypergeometric pFq]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:34, 8 June 2016
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.
