Abstract
This chapter discusses certain problems and prospects for basic hypergeometric functions. It also focuses on finite linear homogeneous ordinary q-difference equations with coefficients that are polynomials in x and q, which have multiple basic hypergeometric series as solutions. The chapter also presents possible multiple series generalizations of the q-analog of Whipple's theorem. It also focuses on whether there are multiple series q-analogs of well-poised hypergeometric series that specialize to the cases of the quituple product identity, or Winquist's identity or some other multiple theta series that sum to an infinite product. The chapter further reviews MacMahon's master theorem and the Dyson conjecture.
Published Version
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