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

New Jacobi-Like Identities for Z_k Parafermion Characters

We state and prove various new identities involving the Z_K parafermion characters (or level-K string functions) for the cases K=4, K=8, and K=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi theta-function identity (which is the K=2 special case), identities in another class relate the level K>2 characters to the Dedekind eta-function, and identities in a third class relate the K>2 characters to the Jacobi theta-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states.Comment: 72 pages (or 78/2 = 39 pages in reduced format

Stratification Economics and Identity Economics

Stratification economics represents an important new approach devoted to explaining economic inequality in terms of how social groups are separated or stratified along economic lines. This paper combines stratification economics with identity economics to address complications that the phenomenon of intersectionality – people having multiple social group identities – creates for stratification economics. It distinguishes two types of social identities recognized by social psychologists, categorical and relational social identities, and uses this distinction to explain how individuals’ personal identities, understood as ordered sets of social identities, can be seen to be both socially and self-constructed. Individuals order and rank their categorical social identities according to weights they assign to them in interactive social settings in which their role-based relational social identities combine different categorical social identities. Recent research in social psychology in the stigma identity threat literature is then reviewed to distinguish two different ways in which individuals respond to others’ stigmatization of their social groups in interactive settings. The paper argues that individuals respond to stigma by assigning weights to their categorical social group identities in ways that reflect both functional power relationships and stigmatization in a way that on balance tend to reinforce social stratification

On identities involving the sixth order mock theta functions

We present q-series proofs of four identities involving sixth order mock theta functions from Ramanujan's lost notebook. We also show how Ramanujan's identities can be used to give a quick proof of four sixth order identities of Berndt and Chan

Differential identities for parametric correlation functions in disordered systems

Copyright © 2008 The American Physical Society.We derive a family of differential identities for parametric correlation functions in disordered systems by casting them as first- or second-order Ward identities of an associated matrix model. We show that this approach allows for a systematic classification of such identities, and provides a template for deriving higher-order results. We also reestablish and generalize some identities of this type which had been derived previously using a different method

Some vanishing sums involving binomial coefficients in the denominator

Identities involving binomial coeffcients usually arise in situations where counting is carried out in two different ways. For instance, some identities obtained by William Horrace [1] using probability theory turn out to be special cases of the Chu-Vandermonde identities. Here, we obtain some generalizations of the identities observed by Horrace and give different types of proofs; these, in turn, give rise to some other new identities. In particular, we evaluate sums of the form Pm j=0 (1) j j d (mj) (n+jj ) and deduce that they vanish when d is even and m = n > d=2. It is well-known [2] that sums involving binomial coeffcients can usually be expressed in terms of the hypergeometric functions but it is more interesting if such a function can be evaluated explicitly at a given argument. Identities such as the ones we prove could perhaps be of some interest due to the explicit evaluation possible. The papers [3], [4] are among many which deal with identities for sums where the binomial coeffcients occur in the denominator and we use similar methods here