2Phi1(q,-1;-q;z)=1+2Sum z^k/(1+q^k)

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Theorem

The following formula holds: $${}_2\phi_1(q,-1;-q;z)=1+2\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{1+q^k},$$ where ${}_2\phi_1$ denotes basic hypergeometric phi.

Proof

References

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