Difference between revisions of "Q-exponential e sub q"

From specialfunctionswiki
Jump to: navigation, search
(Created page with "a")
 
 
(16 intermediate revisions by the same user not shown)
Line 1: Line 1:
a
+
The $q$-exponential $e_q$ is defined for $|z|<1$ by the formula
 +
$$e_q(z) =\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{(q;q)_k},$$
 +
where $(q;q)_k$ denotes the [[q-shifted factorial]]. Note that this function is different than the [[q-exponential e sub 1/q |$q$-exponential $e_{\frac{1}{q}}$]].
 +
 
 +
=Properties=
 +
[[Exponential e in terms of basic hypergeometric phi]]
 +
 
 +
[[Q-Euler formula for e sub q]]
 +
 
 +
=References=
 +
* {{PaperReference|q-Special functions, a tutorial|1994|Tom H. Koornwinder|prev=findme|next=findme}}
 +
 
 +
[[Category:SpecialFunction]]

Latest revision as of 03:30, 21 December 2016

The $q$-exponential $e_q$ is defined for $|z|<1$ by the formula $$e_q(z) =\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{(q;q)_k},$$ where $(q;q)_k$ denotes the q-shifted factorial. Note that this function is different than the $q$-exponential $e_{\frac{1}{q}}$.

Properties

Exponential e in terms of basic hypergeometric phi

Q-Euler formula for e sub q

References