Difference between revisions of "Relationship between sinh and hypergeometric 0F1"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\sinh(az)=az {}_0F_1 \left( ; \dfrac{3}{2} ; \dfrac{(az)^2}{4} \right),$$ | $$\sinh(az)=az {}_0F_1 \left( ; \dfrac{3}{2} ; \dfrac{(az)^2}{4} \right),$$ | ||
where $\sinh$ denotes the [[sinh|hyperbolic sine]] and ${}_0F_1$ denotes the [[hypergeometric pFq]]. | where $\sinh$ denotes the [[sinh|hyperbolic sine]] and ${}_0F_1$ denotes the [[hypergeometric pFq]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:53, 8 June 2016
Theorem
The following formula holds: $$\sinh(az)=az {}_0F_1 \left( ; \dfrac{3}{2} ; \dfrac{(az)^2}{4} \right),$$ where $\sinh$ denotes the hyperbolic sine and ${}_0F_1$ denotes the hypergeometric pFq.
