Difference between revisions of "Exponential e in terms of basic hypergeometric phi"
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The following formula holds: | 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 | + | where $e_q$ is the [[Q-exponential e | $q$-exponential $e$]] and ${}_1\phi_0$ denotes the [[basic hypergeometric phi]]. |
==Proof== | ==Proof== | ||
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.
