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

Correlated X-ray and Optical Variability in Mkn 509

We present results of a 3 year monitoring campaign of the Seyfert 1 galaxy Markarian 509, using X-ray data from the Rossi X-ray Timing Explorer (RXTE) and optical data taken by the SMARTS consortium. Both light curves show significant variations, and are strongly correlated with the optical flux leading the X-ray flux by 15 days. The X-ray power spectrum shows a steep high-frequency slope of -2.0, breaking to a slope of -1.0 at at timescale of 34 days. The lag from optical to X-ray emission is most likely caused by variations in the accretion disk propagating inward.Comment: 13 pages, 3 figures. Accepted for publication in the Astrophysical Journa

Pursuing the Longevity Dividend

The aging of humanity is about to experience a radical change as the demographic transformation to an older world is approaching its final stage. In recent decades, scientists have learned enough about the biological aging processes that many believe it will become possible to slow aging in humans. We contend that the social, economic, and health benefits that would result from such advances may be thought of as “longevity dividends,” and that they should be aggressively pursued as the new approach to health promotion and disease prevention in the 21st century. The time has arrived for governments and national and international healthcare organizations to make research into healthy aging a major research priority.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75679/1/annals.1396.050.pd

Radio Variability of Radio Quiet and Radio Loud Quasars

The majority of quasars are weak in their radio emission, with flux densities comparable to those in the optical, and energies far lower. A small fraction, about 10%, are hundreds to thousands of times stronger in the radio. Conventional wisdom holds that there are two classes of quasars, the radio quiets and radio louds, with a deficit of sources having intermediate power. Are there really two separate populations, and if so, is the physics of the radio emission fundamentally different between them? This paper addresses the second question, through a study of radio variability across the full range of radio power, from quiet to loud. The basic findings are that the root mean square amplitude of variability is independent of radio luminosity or radio-to-optical flux density ratio, and that fractionally large variations can occur on timescales of months or less in both radio quiet and radio loud quasars. Combining this with similarities in other indicators, such as radio spectral index and the presence of VLBI-scale components, leads to the suggestion that the physics of radio emission in the inner regions of all quasars is essentially the same, involving a compact, partially opaque core together with a beamed jet.Comment: 32 pages, 9 figures. Astrophysical Journal, in pres

Subject preferences of fifth-grade children.

Thesis (Ed.M.)--Boston University N.B.:Pages 155 and 309 are missing from original thesis