Relationship between sine and hypergeometric 0F1

From specialfunctionswiki
Revision as of 18:21, 20 May 2015 by Tom (talk | contribs) (Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\sin(z)=z{}_...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Theorem: The following formula holds: $$\sin(z)=z{}_0F_1 \left(;\dfrac{3}{2};-\dfrac{z^2}{4} \right),$$ where $\sin$ denotes the sine and ${}_0F_1$ denotes the hypergeometric pFq.

Proof: