In this work, we explore ramifications and extensions of a $q$-difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. In special cases these symmetric polynomials reduce to well-known classes of orthogonal polynomials. A number of basic properties of these polynomials follow from our approach. This leads naturally to the evaluation of the Askey-Wilson integral and generalizations. We also find expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials. This provides us with a quick route to understanding the group structure generated by iterating the two-term transformations of these functions. We also lay some infrastructure for more general investigations in the future.

q-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions (Memoirs of the American Mathematical Society)

Science & Math

Bowman, Douglas

Mathematics

Amer Mathematical Society

<p>Market Response and Marketing Mix Models takes a forward-looking perspective identifying research opportunities related to market response and marketing mix models falling under four broad areas: • "New" or under-studied inputs and/or "richer" measures of inputs constructs. • Explicitly accounting for the process linking inputs to outputs • "New" or under-studied dependent variables • Under-studied or emerging contexts. Each section covers three broad areas related to marketing mix models - data issues and requirements, methodologies (i.e., traditional econometrics; Bayesian methods; structural models), and substantive findings. As quantitative information about markets and marketing actions has become widely available, modern marketing is presented with both a challenge and an opportunity: how to analyze this information accurately and efficiently, and how to use it to enhance marketing productivity. Market Response and Marketing Mix Models describes the tools needed for achieving these objectives.</p>

Market Response and Marketing Mix Models: Trends and Research Opportunities (Foundations and Trends(r) in Marketing)

Business & Money

Gatignon, Professor Hubert

Economics

Now Publishers

<p>A real life personal tragedy turns into a hope filled story for an 18 year old single mother, merely existing on crutches in the bush of Mozambique. Two writers minding their own book stumble on her story, 217 words in National Geographic article. A remarkable series of events brings together high school students, university seniors, a Handicapped International deminer and his wife, and a 79 year old Indian 'Gandhi.' From three continents the players enter the drama to do impossible. This story will restore your faith in humanity and call you to join a movement to restore dignity and justice to 10,000 innocent ones in Mozambique.</p>

Florencia - An Accidental Story

Biographies & Memoirs

Mullen, John

Leaders & Notable People

Best Seller Publishing, LLC

See the best price to sell, buy, or rent books by Bowman, Douglas. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Bowman, Douglas