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

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==Theorem==
<strong>[[Relationship between cosh and hypergeometric 0F1|Theorem]]:</strong> The following formula holds:
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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]].
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<strong>Proof:</strong> █
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==Proof==
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==References==
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[[Category:Theorem]]
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[[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.

Proof

References