Difference between revisions of "Q-exponential e sub 1/q"
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(Created page with "The $q$-exponential $e_{\frac{1}{q}}$ is an entire function and is defined for $0 < |q| < 1$ by $$e_{\frac{1}{q}}(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{q^{ {k \choose...") |
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$$e_{\frac{1}{q}}(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{q^{ {k \choose 2} }}{(1;q)_k} z^k,$$ | $$e_{\frac{1}{q}}(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{q^{ {k \choose 2} }}{(1;q)_k} z^k,$$ | ||
where ${n \choose 2}$ denotes the [[binomial coefficient]] and $(1;q)_k$ is the [[q-Pochhammer]] symbol. | where ${n \choose 2}$ denotes the [[binomial coefficient]] and $(1;q)_k$ is the [[q-Pochhammer]] symbol. | ||
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| + | [[Category:SpecialFunction]] | ||
Revision as of 18:55, 24 May 2016
The $q$-exponential $e_{\frac{1}{q}}$ is an entire function and is defined for $0 < |q| < 1$ by $$e_{\frac{1}{q}}(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{q^{ {k \choose 2} }}{(1;q)_k} z^k,$$ where ${n \choose 2}$ denotes the binomial coefficient and $(1;q)_k$ is the q-Pochhammer symbol.
