Dougall-Ramanujan Identity
Discovered by Ramanujan 
around 1910. From Hardy (1959, pp. 102-103),
 | |
 | (1) |
 | (2) |
 | (3) |
). This can be rewritten as | |
 | (4) |
In a more symmetric form, if 
, 
, 
, and 
for 
, 2, ..., 6, then
 | |
 | (5) |
is the Pochhammer Symbol (Petkovsek et al. 1996).The identity is a special case of Jackson's Identity.
See also Dixon's Theorem, Dougall's Theorem, Generalized Hypergeometric Function, HypergeometricFunction, Jackson's Identity, Saalschütz's Theorem
References
Dixon, A. C. ``Summation of a Certain Series.'' Proc. London Math. Soc. 35, 285-289, 1903. Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1959. Petkovsek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A. K. Peters, pp. 43, 126-127, and 183-184, 1996.
- Modulus (Congruence)
- Modulus (Elliptic Integral)
- Modulus (Quadratic Invariants)
- Modulus (Set)
- Moessner's Theorem
- Mohammed Sign
- Mollweide Projection
- Mollweide's Formulas
- Moment
- Momental Skewness
- Moment-Generating Function
- Monad
- Money-Changing Problem
- Monge-Ampère Differential Equation
- Monge Patch
- Monge's Chordal Theorem
- Monge's Form
- Monge's Problem
- Monge's Shuffle
- Monge's Theorem
- Monica Set
- Monic Polynomial
- Monkey and Coconut Problem
- Monkey Saddle
- Monochromatic Forced Triangle