Fine's Equation

The q-series identity

			(1)
			(2)
			(3)
			(4)

where  is a q-Pochhammer symbol,  is the number of divisors of  that are congruent to 1, 5, 7, and 11

(mod 24) minus the number of divisors of  congruent to , , , and  (mod 24), and  is a Kronecker symbol.

REFERENCES:

Andrews, G. E. (Ed.). Percy Alexander MacMahon: Collected Papers, Vol. 2. Cambridge, MA: MIT Press, p. 260, 1986.

Andrews, G. E. "Nathan Fine, 1916-1994." Not. Amer. Math. Soc. 42, 678-679, 1995.

Sloane, N. J. A. Sequence A000377 in "The On-Line Encyclopedia of Integer Sequences."