A System of Multivariable Krawtchouk Polynomials and a Probabilistic Application

The one variable Krawtchouk polynomials, a special case of the $_2F_1$ function did appear in the spectral representation of the transition kernel for a Markov chain studied a long time ago by M. Hoare and M. Rahman. A multivariable extension of this Markov chain was considered in a later paper by these authors where a certain two variable extension of the $F_1$ Appel function shows up in the spectral analysis of the corresponding transition kernel. Independently of any probabilistic consideration a certain multivariable version of the Gelfand-Aomoto hypergeometric function was considered in papers by H. Mizukawa and H. Tanaka. These authors and others such as P. Iliev and P. Tertwilliger treat the two-dimensional version of the Hoare-Rahman work from a Lie-theoretic point of view. P. Iliev then treats the general $n$-dimensional case. All of these authors proved several properties of these functions. Here we show that these functions play a crucial role in the spectral analysis of the transition kernel that comes from pushing the work of Hoare-Rahman to the multivariable case. The methods employed here to prove this as well as several properties of these functions are completely different to those used by the authors mentioned above

A Probablistic Origin for a New Class of Bivariate Polynomials

We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresponding to a bivariate Markov chain with a transition kernel formed by a convolution of simple binomial and trinomial distributions. The solution of the relevant eigenfunction problem, giving the spectral resolution of the kernel, leads to what we believe to be a new class of orthogonal polynomials in two discrete variables. Possibilities for the extension of this approach are discussed.Comment: This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Some generating functions for the associated Askey-Wilson polynomials

AbstractAn integral representation is obtained for one family of associated Askey-Wilson polynomials in terms of the ordinary Askey-wilson polynomials. This representation is then used to derive two generating functions for these associated polynomials

Advertising to bottom of the pyramid consumers: descriptive analysis of CSR advertising

The paper aims to understand through primary research the effectiveness of advertising where corporate social responsibility (CSR) messages are given in an international marketing context in a developing country. The work would benefit marketers devise their international marketing strategy and would give new insights into positioning a brand strategically in the developing world. The discussion is on the practice of Telenor, a Norwegian telecommunications company in Bangladesh, a South East Asian country. Other than the commonly perceived utility of corporate reputation management and risk reduction, CSR can contribute to individual brand identity development. A company that integrates CSR in its business operations and strategies may increase sales and market share and strengthen the image and positioning of its brands. Communicating CSR activities is a way of strengthening a brand, but literature is not definitive as to the nature of CSR communication and few experimental studies have been undertaken to understand the overall impact where CSR is a major focus in advertising. Moreover, there are very few research studies undertaken in the context of developing countries involving large low income consumer groups conceptualized as Bottom of the Pyramid consumers whose understanding and perceptions toward CSR may vary from that of the developed world. The paper aims to fill in this gap

Rural consumers' adoption of CRM in a developing country context

This paper illustrates how understanding consumer preferences through market research may enhance CRM adoption among the rural customers of a developing country like Bangladesh. It presents the case of Community Information Centre (CIC) established by Grameenphone, a company owned by Telenor, the Norwegian telecommunications company and Grameen Bank, the Nobel prize winning micro credit organisation in the rural settings of Bangladesh. The paper shows that CIC is an innovative way of building and maintaining customer relationships and technological interface with the financially constrained consumers in a poor developing economy like Bangladesh