Difference between revisions of "Q-exponential E sub 1/q"

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=Properties=
 
=Properties=
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[[Q-difference equation for q-exponential E sub 1/q]]<br />
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<strong>Theorem:</strong> The following formula holds:
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$$D_q E_{\frac{1}{q}}(az)=aE_{\frac{1}{q}}(qaz),$$
 
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where $D_q$ denotes the [[q-difference operator]] and $E_{\frac{1}{q}}$ denotes the [[Q-exponential E sub 1/q|$q$-exponential $E_{\frac{1}{q}}$]].
 
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<strong>Proof:</strong> █
 
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=References=
 
=References=

Revision as of 22:47, 16 June 2016

The $E_{\frac{1}{q}}$ function is defined by the formula $$E_{\frac{1}{q}}(z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{q^{ {k \choose 2} }}{[k]_q!} z^k.$$

Properties

Q-difference equation for q-exponential E sub 1/q


References

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