Orthogonal polynomials and continued fractions arising from contiguous relations and generalizations of Kummer and q-Kummer identities - Mansour, Zeinab S. I. (The Ramanujan journal, 2019)
In this paper, we show formally how can we generate continued fractions starting from three-term contiguous relations. Then as examples, starting from certain contiguous relations for 2 F 1 and 2 ϕ 1 , we derive orthogonal polynomials, continued fractions and in case of 2 F 1 , the measure of orthogonality. Also, a generalization of q -Kummer’s identity is introduced.