On a remarkable formula of Ramanujan

A simple proof of Ramanujan's formula for the Fourier transform of the square of the modulus of the Gamma function restricted to a vertical line in the right half-plane is given. The result is extended to vertical lines in the left half-plane by solving an inhomogeneous ODE. We then use it to calculate the jump across the imaginary axis.Comment: To appear in Archiv der Mathemati

Reflections on Euler's reflection formula and an additive analogue of Legendre's duplication formula

In this note, we look at some of the less explored aspects of the gamma function. We provide a new proof of Euler's reflection formula and discuss its significance in the theory of special functions. We also discuss a result of Landau concerning the determination of values of the gamma function using functional identities. We show that his result is sharp and extend it to complex arguments. In 1848, Oskar Schl\"omilch gave an interesting additive analogue of the duplication formula. We prove a generalized version of this formula using the theory of hypergeometric functions

Isolation and characterization of Newcastle disease virus from vaccinated commercial layer chicken

Aim: Newcastle disease (ND) is an infectious, highly contagious and destructive viral disease of poultry and controlled by vaccination. In spite of vaccination, incidence of ND was reported in commercial layers with gastrointestinal lesions. This study was undertaken to assess the prevalence and pathotypes of Newcastle disease virus (NDV) involved in gastrointestinal tract abnormalities of vaccinated commercial layer chicken of Namakkal region for a period of three years from 2008 and 2011. Materials and Methods: Pooled tissue (trachea, lung, spleen, proventriculus, intestine and caecal tonsils) samples collected from dead birds on postmortem examination from 100 layer flocks above 20 weeks of age with gastrointestinal lesions were subjected to isolation of NDV in embryonated specific pathogen free (SPF) chicken eggs. Mean death time (MDT) and intracerebral pathogenicity index of the isolates were characterized. Flock details were collected from NDV positive flocks to assess the prevalence and impact of NDV on vaccinated commercial layer chicken. Results: Among the 100 flocks examined Newcastle disease virus was detected in 14 flocks as a single infection and 10 flocks as combined infections with worm infestation, necrotic enteritis and coccidiosis. Chicken embryo mean death time (MDT) and intracerebral pathogenicity index (ICPI) values ranged from 50.4 to 96.0 hrs and from 0.650 to 1.675 respectively. Affected birds showed anorexia, diarrohea and drop in egg production. Macropathologically, matting of vent feathers, petechial haemorrhage on the tip of proventricular papilla, caecal tonsils and degeneration of ovarian follicles were noticed. The incidence of ND was most commonly noticed in 20-50 wk of age and between the months of September to November. Morbidity rate varied from 5% to 10% in the NDV alone affected flocks and 5 to 15% in NDV with other concurrent infections. Egg production drop from the expected level ranged between 3 to 7 % in ND and 5 to 10 % in concurrent infections. Average mortality in NDV and concurrently affected (NDV and Coccidiosis) flocks were 2.89% and 3.50 % respectively. Conclusion: The present study revealed 24 % of gastrointestinal tract abnormalities in commercial layer chicken were caused by various pathotypes of Newcastle disease virus. The virus caused the disease as single and concurrently with other diseases. Vaccination minimized the clinical manifestation and lesions even in velogenic virus affected flocks

Salmonella enterica Serovar Typhimurium Lacking hfq Gene Confers Protective Immunity against Murine Typhoid

Salmonella enterica is an important enteric pathogen and its various serovars are involved in causing both systemic and intestinal diseases in humans and domestic animals. The emergence of multidrug-resistant strains of Salmonella leading to increased morbidity and mortality has further complicated its management. Live attenuated vaccines have been proven superior over killed or subunit vaccines due to their ability to induce protective immunity. Of the various strategies used for the generation of live attenuated vaccine strains, focus has gradually shifted towards manipulation of virulence regulator genes. Hfq is a RNA chaperon which mediates the binding of small RNAs to the mRNA and assists in post-transcriptional gene regulation in bacteria. In this study, we evaluated the efficacy of the Salmonella Typhimurium Δhfq strain as a candidate for live oral vaccine in murine model of typhoid fever. Salmonella hfq deletion mutant is highly attenuated in cell culture and animal model implying a significant role of Hfq in bacterial virulence. Oral immunization with the Salmonella hfq deletion mutant efficiently protects mice against subsequent oral challenge with virulent strain of Salmonella Typhimurium. Moreover, protection was induced upon both multiple as well as single dose of immunizations. The vaccine strain appears to be safe for use in pregnant mice and the protection is mediated by the increase in the number of CD4+ T lymphocytes upon vaccination. The levels of serum IgG and secretory-IgA in intestinal washes specific to lipopolysaccharide and outer membrane protein were significantly increased upon vaccination. Furthermore, hfq deletion mutant showed enhanced antigen presentation by dendritic cells compared to the wild type strain. Taken together, the studies in murine immunization model suggest that the Salmonella hfq deletion mutant can be a novel live oral vaccine candidate