1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z)
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Theorem
The following formula holds: $${}_1\phi_0(a;;z){}_1\phi_0(b;;z)={}_1\phi_0(ab;;z),$$ where ${}_1\phi_0$ denotes basic hypergeometric phi.
Proof
References
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $4.8 (5)$