Implementation of summation theorems of Andrews and Gessel-Stanton

Generalized hypergeometric functions and their natural generalizations in one and several variables appear in many mathematical problems and their applications. Solving partial differential equations encountered in many applied problems of mathematics physics is expressed in terms of such generalized hypergeometric functions. In particular, the Srivastava-Daoust double hypergeometric function (S-D function) has proved its practical utility in representing solutions to a wide range of problems in pure and applied mathematics. In this paper, we introduce two general double-series identities involving bounded sequences of arbitrary complex numbers employing the finite summation theorems of Gessel-Stanton and Andrews for terminating 3F2 hypergeometric series with arguments 3/4 and 4/3, respectively. Using these double-series identities, we establish two reduction formulas for the (S-D function) with arguments z, 3z/4 and z, −4z/3 expressed in terms of two generalized hypergeometric function of arguments proportional to z3 and −z3 respectively. All the results mentioned in the paper are verified numerically using Mathematica Program

Some Convergent Summation Theorems For Appell’s Function F1 Having Arguments −1, 1/2

In this paper, we obtain some closed forms of hypergeometric summation theorems for Appell’s function of first kind F1 having the arguments −1, 1/2 with suitable convergence conditions, by adjustment of parameters and arguments in generalized form of first, second and third summation theorems of K¨ummer and others

Summation of some infinite series by the methods of Hypergeometric functions and partial fractions

In this article we obtain the summations of some infinite series by partial fraction method and by using certain hypergeometric summation theorems of positive and negative unit arguments, Riemann Zeta functions, polygamma functions, lower case beta functions of one-variable and other associated functions. We also obtain some hypergeometric summation theorems for: 8F7[9/2, 3/2, 3/2, 3/2, 3/2, 3, 3, 1; 7/2, 7/2, 7/2, 7/2, 1/2, 2, 2; 1], 5F4[5/3, 4/3, 4/3, 1/3, 1/3; 2/3, 1, 2, 2; 1], 5F4[9/4, 5/2, 3/2, 1/2, 1/2; 5/4, 2, 3, 3; 1], 5F4[13/8, 5/4, 5/4, 1/4, 1/4; 5/8, 2, 2, 1; 1], 5F4[1/2, 1/2, 5/2, 5/2, 1; 3/2, 3/2, 7/2, 7/2; -1], 4F3[3/2, 3/2, 1, 1; 5/2, 5/2, 2; 1], 4F3[2/3, 1/3, 1, 1; 7/3, 5/3, 2; 1], 4F3[7/6, 5/6, 1, 1; 13/6, 11/6, 2; 1] and 4F3[1, 1, 1, 1; 3, 3, 3; -1]

Some Convergent Summation Theorems For Appell’s Function F1 Having Arguments −1, 1/2

In this paper, we obtain some closed forms of hypergeometric summation theorems for Appell’s function of first kind F1having the arguments -1, 1/2 with suitable convergence conditions, by adjustment of parameters and arguments in generalized form of first, second and third summation theorems of Ku¨mmer and others

A family of definite integrals involving Legendre’s polynomials

The main objective of this article is to provide the analytical solutions (not previously found and not available in the literature) of some problems related with definite integrals integrands of which are the products of the derivatives of Legendre’s polynomials of first kind having different order, with the help of some derivatives of Legendre’s polynomials of first kind Pn(x), Rodrigues formula, Leibnitz’s generalized rule for successive integration by parts and certain values of successive differential coefficients of (x2-1)r at x = ±1

Summation of some infinite series by the methods of Hypergeometric functions and partial fractions

In this article we obtain the summations of some infinite series by partial fraction method and by using certain hypergeometric summation theorems of positive and negative unit arguments, Riemann Zeta functions, polygamma functions, lower case beta functions of one-variable and other associated functions. We also obtain some hypergeometric summation theorems for: 8F7[9/2, 3/2, 3/2, 3/2, 3/2, 3, 3, 1; 7/2, 7/2, 7/2, 7/2, 1/2, 2, 2; 1], 5F4[5/3, 4/3, 4/3, 1/3, 1/3; 2/3, 1, 2, 2; 1], 5F4[9/4, 5/2, 3/2, 1/2, 1/2; 5/4, 2, 3, 3; 1], 5F4[13/8, 5/4, 5/4, 1/4, 1/4; 5/8, 2, 2, 1; 1], 5F4[1/2, 1/2, 5/2, 5/2, 1; 3/2, 3/2, 7/2, 7/2; −1], 4F3[3/2, 3/2, 1, 1; 5/2, 5/2, 2; 1], 4F3[2/3, 1/3, 1, 1; 7/3, 5/3, 2; 1], 4F3[7/6, 5/6, 1, 1; 13/6, 11/6, 2; 1] and 4F3[1, 1, 1, 1; 3, 3, 3; −1]

Fragmentation of very high energy heavy ions

A stack of CR39 (C12H18O7)n nuclear track detectors with a Cu target was exposed to a 158 A GeV lead ion beam at the CERN-SPS, in order to study the fragmentation properties of lead nuclei. Measurements of the total, break-up and pick-up charge-changing cross sections of ultrarelativistic Pb ions on Cu and CR39 targets are presented and discussed.Comment: 4 pages, 3 EPS figures included with epsf, uses article.sty Talk presented by M. Giorgini at the Int. Conf. on Structure of the Nucleus at the Dawn of the Century, Bologna (Italy), May 29-June 3, 200

Search for magnetic monopoles at the Chacaltaya cosmic ray laboratory

The new large area (400 m2) experiment—SLIM—to search for magnetic monopoles and other exotic massive particles is presented. It uses of nuclear track detectors and is being deployed at the Chacaltaya cosmic ray laboratory for at least 4 years. The detection capability of the experiment is discussed

Biochemical profile and in vitro neuroprotective properties of Carpobrotus edulis L., a medicinal and edible halophyte native to the coast of South Africa

This work reports the nutritional profile and in vitro neuroprotective properties of leaves of Carpobrotus edulis L, a medicinal and edible succulent species native to the coast of South Africa. Biomass was evaluated for proximate composition and for contents in carotenoids, liposoluble pigments and minerals. Hexane, dichloromethane, ethyl acetate and methanol extracts were prepared by Soxhlet extraction from dried biomass and evaluated for in vitro inhibition of acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE), capacity to attenuate hydrogen peroxide (H2O2)-induced injury in the human dopaminergic cell line SH-SY5Y and for anti-neuroinflammatory potential on lipopolysaccharide (LPS)-stimulated microglia cells. Extracts were evaluated for antioxidant activity by four complementary methods, total content of phenolics, tannins and flavonoids. Finally the profile of the main phenolic compounds was determined by high performance liquid chromatography with diode array detection (HPLC-DAD). C edulis has a high moisture content, high levels of crude protein, fibre, ash, carotenoids, calcium and iron and a low fat level. The extracts were able to efficiently scavenge the free radical 2,2-diphenyl-1-picrylhydrazyl (DPPH), reduce iron and chelate copper and iron ions, and exhibited different levels of phenolic compounds in the order ethyl acetate > methanol > dichloromethane > hexane. The main compounds detected were gallic and salicylic acids and quercetin, all in the ethyl acetate extract. The extracts allowed a dual and potent inhibition of AChE and BuChE. The dichloromethane and methanol extracts had the strongest capacity to prevent cell death induced by H2O2, and the methanol extract had anti-neuronflammatory properties. All together our results suggest that consumption of leaves of C edulis can contribute for a balanced diet, and that they may add to the improvement of cognitive functions. It also suggests possible novel biotechnological applications of C. edulis such as source of molecules and/or products for the food and/or pharmaceutical industries. Studies aiming to the isolation and identification of the bioactive compounds are already in progress. (C) 2017 SAAB. Published by Elsevier B.V. All rights reserved.Portuguese National BudgetXtremeGourmet project [ALG-01-0247-FEDER-017676]FCT Investigator Programme [IF/00049/2012]info:eu-repo/semantics/publishedVersio

Operation and performance of the ATLAS semiconductor tracker

The semiconductor tracker is a silicon microstrip detector forming part of the inner tracking system of the ATLAS experiment at the LHC. The operation and performance of the semiconductor tracker during the first years of LHC running are described. More than 99% of the detector modules were operational during this period, with an average intrinsic hit efficiency of (99.74±0.04)%. The evolution of the noise occupancy is discussed, and measurements of the Lorentz angle, δ-ray production and energy loss presented. The alignment of the detector is found to be stable at the few-micron level over long periods of time. Radiation damage measurements, which include the evolution of detector leakage currents, are found to be consistent with predictions and are used in the verification of radiation background simulations