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Basic q-series

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Post Wed Jul 24, 2013 12:51 pm
zaidalyafey User avatar
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Prove the following

\(\displaystyle \lim_{q \to 1}\frac{(a)_{\infty}}{(aq^x)_{\infty}}=(1-a)^x\)
\(\displaystyle \sum_{k\geq 0}\frac{f^{(k)} (s)}{(s+1)_k} (-s)^{k}= \int^{1}_0x^{s} f(s x) \left( \frac{x}{s}\right) \, dx\)


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Post Wed Jul 31, 2013 3:41 pm
zaidalyafey User avatar
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It can be solved using the q-binomial theorem . If someone is interested I can show it.
\(\displaystyle \sum_{k\geq 0}\frac{f^{(k)} (s)}{(s+1)_k} (-s)^{k}= \int^{1}_0x^{s} f(s x) \left( \frac{x}{s}\right) \, dx\)


Wanna learn what we discuss , see tutorials

Post Sun May 18, 2014 6:46 pm

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Location: Bournemouth, United Kingdom
zaidalyafey wrote:
It can be solved using the q-binomial theorem . If someone is interested I can show it.


I am interested.

Post Sun May 18, 2014 7:32 pm
zaidalyafey User avatar
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\(\displaystyle \sum_{k\geq 0}\frac{f^{(k)} (s)}{(s+1)_k} (-s)^{k}= \int^{1}_0x^{s} f(s x) \left( \frac{x}{s}\right) \, dx\)


Wanna learn what we discuss , see tutorials


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