 About 2,920 results  books.google.com 
 books.google.com DougallRamanujan Identity where 5F4(a,b,c,d,e; f,g,h, i, z) is a GENERALIZED
HYPERGEOMETRIC FUNCTION and T(z) is the GAMMA FUNCTION. Bailey (
1935, pp. 25–6) called the DOUGALLRAMANUJAN IDENTITY "Dougall's
theorem. 

 books.google.com In Chapter 2, we showed that the latter result, known as Dixon's theorem, is a
consequence of Dougall's theorem. See Remark 2.2.2 in Chapter 2. Because
Dougall's theorem is itself a corollary of Whipple's transformation, it would be nice
if we ... 

 books.google.com Corollary 1 may also be proved with the aid of Dougall's theorem. However,
Dougall's theorem is not applicable to Entry 2. The next entry is also an instance
of Dougall's theorem. Entry 3. Let <x, /$, y, and 6 be complex 14. Infinite Series
247. 

 books.google.com (Finish this proof!). Moreover, given the lefthand side of Dixon's theorem, we
have deduced its righthand side. What about Dougall's Theorem? Can we
derive the righthand side of Dougall's identity directly from the lefthand sum?
Here is the ... 

 books.google.com The evaluation (3) is a special instance of a limiting case of Dougall's theorem,
namely Corollary 5 in Section 7 of Chapter 10 in the second notebook (Berndt [35
, pp. 16, 2324]). Both of these observations were first made by Hardy [99], [100, ... 

 books.google.com As an example, Dougall's theorem summing a terminating ^Fg of unit argument
generalizes to Jackson's theorem for terminating s $7 of argument z = q. We shall
now show that the basic hypergeometric series at root of unity are intimately ... 

 books.google.com Jonathan M. Borwein  1997  Preview SIAM J. Math. Anal, 13:295308, 1982. [9] T. H. Koornwinder. On Zeilberger's
algorithm and its ganalogue. J. Comp. and Appl. Math., 48:91111, 1993. [10] A.
Lakin. A hypergeometric identity related to Dougall's theorem. George E.
Andrews. 

 books.google.com Corollary (F. H. Jackson's ganalog of Dougall's theorem [24], [23; p. 35, eq. (2.6.
2)]) g (oqt"» 03 03 aql~n \ *~' P< ' P2 ' kpw'q)n Proof. This is just the assertion that
the WPBailey pair a'n(a, k) and /%(a, A;) defined from Theorem 7 satisfy (6.2) ... 

 books.google.com The aforementioned identity of Jackson is the qanalogue of Dougall's theorem
and is given by [16, p. 67] 15.1) f7 a, q/a, q^, b, c, d, e, q ,/a, /a, aq/b, aq/c, aq/d,
aq/e, aq (aq)N(aq/cd)N(aq/bd)N(aq/bc)N (aq/b)N(aq/c)N(aq/d)N(aq/bcd)N '
where ... 

 