Difference between revisions of "Relationship between sine and hypergeometric 0F1"
From specialfunctionswiki
| Line 1: | Line 1: | ||
| − | + | ==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== | |
Revision as of 00:38, 4 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.
