Abstract
This chapter focuses on positivity and special functions. The solutions of many problems depend on the determination of when a specific function is positive or nonnegative. In many cases, a series or integral representation for the function can be derived in terms of more elementary functions. Sometimes the problem can be reduced to a simpler one involving fewer parameters or it can be transformed into another problem that is easier to handle. Various hypergeometric series representations for the Hahn polynomials are used to write a sum of products of gamma functions. The chapter also describes absolutely monotonic and completely monotonic functions.
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