The last of the hypergeometric continued fractions
David R. Masson
Abstract
A contiguous relation for complementry pairs of very well poised balanced 10ϕ9 basic hypergeometric functions is used to derive an explict expression for the associated continued fraction. This generalizes the continued fraction results associated with both Ramanujan's Entry 40 and Askey-Wilson polynomials which can be recovered as limits. Associated with our continued fraction results there are systems of biorthogonal rational functions that have yet to be derived.
Create a lesson
Related papers
Optimal fractional discrete Hardy inequalities on the half-line
František Štampach, Jakub Waclawek
Capacitary-Distance Hardy Inequality
Yiqun Chen, Jie Xiao, Dachun Yang et al.
Microstructure evolution as a game
Michael Ortiz
Optimal differentiability of isotropic positive definite functions on even-dimensional spheres
Yan Ge
Bilinear Bochner--Riesz Means on the Complex Sphere
S. Bagchi, Md N. Molla, J. Singh et al.
Exact-Support Counterexamples to Euclidean-to-Spherical Transfer of Positive Definiteness in Even Dimensions
Wentao Huang, Haizhang Zhang