Author: George Gasper
Abstract: q-Analogues of Erdélyi's fractional integral representations of hypergeometric functions are derived and extended to expansion formulas for certain 3\phi2 and 4\phi2 basic hypergeometric series. Special cases of some of the derived formulas are used to derive new summation formulas for double hypergeometric and basic hypergeometric Kampé de Fériet series, including a summation formula for a double basic hypergeometric Kampé de Fériet series that was conjectured in work of J. Van der Jeugt, S.N. Pitre, and K. Srinivasa Rao on the evaluation of the 9-j recoupling coefficients appearing in the quantum theory of angular momentum.
Key words: hypergeometric functions, basic hypergeometric functions and series, fractional integrals, q-fractional integrals, summation formulas, q-Kampé de Fériet series, q-analogues.
1991 Mathematics Subject Classification: Primary 33C65, 33D05, 33D15, 33D20, 33D60, 33D70; Secondary 33C05, 33C20, 33C45, 33D45.