Difference between revisions of "Exponential e in terms of basic hypergeometric phi"
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| − | + | ==Theorem== | |
| − | + | 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]]. | where $e_q$ is the [[Q-exponential e | $q$-exponential $e$]] and ${}_1\phi_0$ denotes the [[basic hypergeometric series phi]]. | ||
| − | + | ||
| − | + | ==Proof== | |
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| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 21:38, 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 series phi.
