Rogers Mod 14 Identities

The Rogers mod 14 identities are a set of three Rogers-Ramanujan-like identities given by

			(1)
			(2)
			(3)
			(4)
			(5)
			(6)
			(7)
			(8)
			(9)

(OEIS A105780, A105781, and A105782).

The -identity was found by Rogers (1894) and appears as formula 61 in the list of Slater (1952). The - and -identities were found by Rogers (1917) and appeared as formulas 60 and 59 respectively in Slater (1952).

REFERENCES:

Mc Laughlin, J.; Sills, A. V.; and Zimmer, P. "Dynamic Survey DS15: Rogers-Ramanujan-Slater Type Identities." Electronic J. Combinatorics, DS15, 1-59, May 31, 2008. http://www.combinatorics.org/Surveys/ds15.pdf.

Rogers, L. J. "Second Memoir on the Expansion of Certain Infinite Products." Proc. London Math. Soc. 25, 318-343, 1894.

Rogers, L. J. "On Two Theorems of Combinatory Analysis and Some Allied Identities." Proc. London Math. Soc. 16, 315-336, 1917.

Slater, L. J. "Further Identities of the Rogers-Ramanujan Type." Proc. London Math. Soc. Ser. 2 54, 147-167, 1952.