Difference between revisions of "Exponential e in terms of basic hypergeometric phi"

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==Theorem==
<strong>[[Exponential e in terms of basic hypergeometric phi|Theorem]]:</strong> The following formula holds:
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The following formula holds:
 
$$e_q(z) = {}_1\phi_0(0;-;q;z),$$
 
$$e_q(z) = {}_1\phi_0(0;-;q;z),$$
where $e_q$ is the [[Q-exponential e | $q$-exponential $e$]] and ${}_1\phi_0$ denotes the [[basic hypergeometric series phi]].
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where $e_q$ is the [[Q-exponential e | $q$-exponential $e$]] and ${}_1\phi_0$ denotes the [[basic hypergeometric phi]].
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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 21:39, 17 June 2017

Theorem

The following formula holds: $$e_q(z) = {}_1\phi_0(0;-;q;z),$$ where $e_q$ is the $q$-exponential $e$ and ${}_1\phi_0$ denotes the basic hypergeometric phi.

Proof

References