Certain transformations and summations for generalized hypergeometric series with integral parameter differences

Certain transformation and summation formulas for generalized hypergeometric series with integral parameter differences are derived

Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x)

We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer. The results derived for the latter are used to obtain Kummer-type transformations for the generalized hypergeometric function 2 F 2(x) and reduction formulas for certain Kampé de Fériet functions. Certain summations for the partial sums of the Gauss hypergeometric series 2 F 1(1) are also obtained

Transformation formulas for the generalized hypergeometric function with integral parameter differences

Transformation formulas of Euler and Kummer-type are derived respectively for the generalized hypergeometric functions r+2Fr+1(x) and r+1Fr+1(x), where r pairs of numeratorial and denominatorial parameters differ by positive integers. Certain quadratic transformations for the former function, as well as a summation theorem when x = 1, are also considered.<br/

Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x)

We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula for r+1 F r+1 (x) that was recently derived in a different way

Narrative and Casuistry: A Response to John Arras

Symposium: Emerging Paradigms in Bioethic

Critical Humanism and the Study of Religion: A Statement and Defense

This essay offers a statement and defense of four core claims of my work, Why Study Religion? Those are: (1) the field of religious studies is preoccupied by procedural methods for studying religion to the neglect of values and purposes that can justify its intellectual practices; (2) this preoccupation operates under a “regime of truth” that is anti-normative; (3) this regime of truth buckles under the pressure of repressed values and smuggles in crypto-normative judgments and commitments; and (4) this preoccupation with method can be remedied by attending to purposes that can justify the study of religion, which I call Critical Humanism. Critical Humanism aims to expand the moral imagination and comprises four values: post-critical reasoning, social criticism, cross-cultural fluency, and environmental responsibility. After describing the book’s main claims, I take up critiques expressed by Michael Stausberg, et al. in their essay, “A Normative Turn in Religious Studies?

Do Teacher Absences Impact Student Achievement? Longitudinal Evidence from One Urban School District

Rates of employee absences and the effects of absences on productivity are topics of conversation in many organizations in many countries. One reason is that high rates of employee absence may signal weak management and poor labor-management relations. A second reason is that reducing rates of employee absence may be an effective way to improve productivity. This paper reports the results of a study of employee absences in education, a large, labor-intensive industry. Policymakers' concern with teacher absence rests on three premises: (1) that a significant portion of teachers' absences is discretionary, (2) that teachers' absences have a nontrivial impact on productivity, and (3) that feasible policy changes could reduce rates of absence among teachers. This paper presents the results of an empirical investigation of the first two of these premises; it discusses the third premise. We employ a methodology that accounts for time-invariant differences among teachers in skill and motivation. We find large variation in adjusted teacher absence rates among schools. We estimate that each 10 days of teacher absences reduce students' mathematics achievement by 3.3 percent of a standard deviation.