Difference between revisions of "Z/(1-sqrt(q))2Phi1(q,sqrt(q);sqrt(q^3);z)=Sum z^k/(1-q^(k-1/2))"
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(Created page with "==Theorem== The following formula holds: $$\dfrac{z}{1-\sqrt{q}} {}_2\phi_1 \left(q,\sqrt{q};\sqrt{q^3};z \right) = \displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{1-q^{k-\frac{1...") |
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Revision as of 21:53, 17 June 2017
Theorem
The following formula holds: $$\dfrac{z}{1-\sqrt{q}} {}_2\phi_1 \left(q,\sqrt{q};\sqrt{q^3};z \right) = \displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{1-q^{k-\frac{1}{2}}},$$ where ${}_2\phi_1$ denotes basic hypergeometric phi.
Proof
References
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $4.8 (8)$
