About 2,920 results
|Dougall-Ramanujan 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 DOUGALL-RAMANUJAN IDENTITY "Dougall's
|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 ...
|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
|(Finish this proof!). Moreover, given the left-hand side of Dixon's theorem, we |
have deduced its right-hand side. What about Dougall's Theorem? Can we
derive the right-hand side of Dougall's identity directly from the left-hand sum?
Here is the ...
|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, 23-24]). Both of these observations were first made by Hardy , [100, ...
|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 ...
Jonathan M. Borwein - 1997 - Preview
|SIAM J. Math. Anal, 13:295-308, 1982.  T. H. Koornwinder. On Zeilberger's |
algorithm and its g-analogue. J. Comp. and Appl. Math., 48:91-111, 1993.  A.
Lakin. A hypergeometric identity related to Dougall's theorem. George E.
|Corollary (F. H. Jackson's g-analog of Dougall's theorem , [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 WP-Bailey pair a'n(a, k) and /%(a, A;) defined from Theorem 7 satisfy (6.2) ...
|The aforementioned identity of Jackson is the q-analogue 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 '