Difference between revisions of "Relationship between sine and hypergeometric 0F1"

From specialfunctionswiki
Jump to: navigation, search
Line 1: Line 1:
<div class="toccolours mw-collapsible mw-collapsed">
+
==Theorem==
<strong>[[Relationship between sine and hypergeometric 0F1|Theorem]]:</strong> The following formula holds:
+
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]].
<div class="mw-collapsible-content">
+
 
<strong>Proof:</strong> █
+
==Proof==
</div>
+
 
</div>
+
==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.

Proof

References