Difference between revisions of "Relationship between cosh and hypergeometric 0F1"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\cosh(az)=az {}_0F_1 \left( ; \dfrac{1}{2}; \dfrac{(az)^2}{4} \right),$$ | $$\cosh(az)=az {}_0F_1 \left( ; \dfrac{1}{2}; \dfrac{(az)^2}{4} \right),$$ | ||
where $\cosh$ denotes the [[cosh|hyperbolic cosine]] and ${}_0F_1$ denotes the [[hypergeometric pFq]]. | where $\cosh$ denotes the [[cosh|hyperbolic cosine]] and ${}_0F_1$ denotes the [[hypergeometric pFq]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 00:01, 17 June 2016
Theorem
The following formula holds: $$\cosh(az)=az {}_0F_1 \left( ; \dfrac{1}{2}; \dfrac{(az)^2}{4} \right),$$ where $\cosh$ denotes the hyperbolic cosine and ${}_0F_1$ denotes the hypergeometric pFq.
