On Somos' dissection identities

AbstractWe give proofs of a list of M. Somos' dissection identities. An eta function identity presented by B.C. Berndt and W.B. Hart, a theorem by H.-C. Chan on the congruence property of a(n) with generating function (q;q)∞−1(q2;q2)∞−1, and a theorem by G.E. Andrews, A. Schilling, and S.O. Warnaar are shown to be related to dissection identities. Several new corollaries are also presented as applications