Trace identities from identities for determinants

We present new identities for determinants of matrices $(A_{i,j})$ with entries $A_{i,j}$ equal to $a_{i,j}$ or $a_{i,0}a_{0,j}-a_{i,j}$, where the $a_{i,j}$'s are indeterminates. We show that these identities are behind trace identities for $SL(2,\Bbb C)$ matrices found earlier by Magnus in his study of trace algebras.Comment: 14 pages, AmS-Te

P-symbols, Heun Identities, and 3F2 Identities

The usefulness of Riemann P-symbols in deriving identities involving the parametrized special function Hl is explored. Hl is the analytic local solution of the Heun equation, the canonical second-order differential equation on the Riemann sphere with four regular singular points. The identities discussed include ones coming from Moebius automorphisms and F-homotopies, and also quadratic and biquadratic transformations. The case when Hl is identical to a generalized hypergeometric function of 3F2 type is examined, and Pfaff and Euler transformations of 3F2(a1,a2,e+1;b1,e;x) are derived. They extend several 3F2 identities of Bailey and Slater.Comment: 20 page

Feminine Identities

The first four essays in this volume all focus on issues of gender in the works of different English authors and thinkers. Shorter versions of each of these essays were formerly presented as papers in an autonomous section of the Research and Educational Programme on Studies of Identity at the XXth Meeting of the Portuguese Association of Anglo-American Studies (Póvoa de Varzim, 1999) and published in the proceedings of the conference. The second cluster of essays in this volume — two of which (Jennie Wang’s and Teresa Cid’s) were first presented, in shorter versions, at the joint ASA/CAAS Conference (Montréal, 1999) — addresses the work of American women variously engaged in contexts of cultural diversity and grappling with the ideas of what it means to be an American and a woman, particularly in the twentieth century. These essays approach, from different angles, the definitional quandaries and semantic difficulties encountered when speaking about the self and the United States and provide, in one way or another, a sort of feminine rewriting of American myths and history.Fundação para a Ciência e a Tecnologi

Hirschhorn's identities

We prove a general identity between power series and use this identity to give proofs of a number of identities proposed by M.D. Hirschhorn. We also use the identity to give proofs of a well-known result of Jacobi, the quintuple-product identity and Winquist's identit