(The contiguous Watson's Theorem) Thank you! The following message has been sent to the *MathWorld* team: *Source URL:* http://mathworld.wolfram.com/WatsonsTheorem.html *E-mail:* billgosper@gmail.com *Name:* --Bill Gosper *Comment type:* ADD *Organization:* dis- *Country:* United States *Comments:* Simply including one contiguous identity, e.g., HypergeometricPFQ[{a, b, c}, {a/2 + b/2, 2 c}, 1] == Sqrt[\[Pi]] Gamma[(a + b)/2] Gamma[1/2 + c] Gamma[ 1/2 (-a - b) + c] (1/( Gamma[a/2] Gamma[(1 + b)/ 2] Gamma[-(a/2) + c] Gamma[(1 - b)/2 + c]) + 1/( Gamma[(1 + a)/2] Gamma[b/ 2] Gamma[(1 - a)/2 + c] Gamma[-(b/2) + c])) lets you add integers to all five parameter slots, via the three-term recurrences. This covers a mere factor of ∞^5 more cases. I can't understand why nobody does this! You should also do it for Dixon, Pfaff, Whipple, Dougall, ... . *MathWorld usage:* weekly *Mathematica usage:* daily