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

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==Theorem==
<strong>[[Relationship between sine and hypergeometric 0F1|Theorem]]:</strong> The following formula holds:
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The following formula holds:
$$\sin(z)=z{}_0F_1 \left(;\dfrac{3}{2};-\dfrac{z^2}{4} \right),$$
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$$\sin(az)=az{}_0F_1 \left(;\dfrac{3}{2};-\dfrac{(az)^2}{4} \right),$$
where $\sin$ denotes the [[sine]] and ${}_0F_1$ denotes the [[hypergeometric pFq]].
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where $\sin$ denotes the [[sine]] function 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 07:34, 8 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