Some results on q-Hermite based hybrid polynomials

In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Euler polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Further, the 2D q-Hermite based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials are introduced and important relations for these polynomials are also established. Finally, a new class of the 2D q-Hermite based Appell polynomials is investigated as the generalization of the above polynomials. The determinant definitions for the 2D q-Hermite based Appell and related polynomials are also explored

Certain Results for the Laguerre-Gould Hopper Polynomials

In this paper, we derive generating functions for the Laguerre-Gould Hopper polynomials in terms of the generalized Lauricella function by using series rearrangement techniques. Further, we derive the summation formulae for that polynomials by using different analytical means on its generating function or by using certain operational techniques. Also, generating functions and summation formulae for the polynomials related to Laguerre-Gould Hopper polynomials are obtained as applications of main results

Autoantibodies in Viral Infections

The immune system’s ability to distinguish self from nonself is essential for initiating host defense against microbial antigens and protection of self-antigens from autoimmune-associated destruction. Virus infections have been implicated in the initiation of multiple human autoimmune diseases. This chapter aims to summarize the main principles for some specific viral infections and the subsequent production of autoantibodies resulting in the initiation, progression, and perpetuation of autoimmune diseases. Various mechanisms by which virus infections can induce autoimmune responses including molecular mimicry and epitope spreading are discussed with respect to these viruses, and evidence implicating virus infections in the pathogenesis of various human autoimmune diseases is reviewed. A better understanding of the viral origin of autoimmune diseases is an important step in the identification of high-risk patients as well as designing prevention and disruption strategies

Euler Type Integrals and Integrals in Terms of Extended Beta Function

We derive the evaluations of certain integrals of Euler type involving generalized hypergeometric series. Further, we establish a theorem on extended beta function, which provides evaluation of certain integrals in terms of extended beta function and certain special polynomials. The possibility of extending some of the derived results to multivariable case is also investigated