Abstract
New expansions for certain 2Fl's as a sum of r higher order hypergeometric series are given. When specialized to the binomial theorem, these r hypergeometric series sum. The results represent cubic and higher order transformations, and only Vandermonde's theorem is necessary for the elementary proof. Some q-analogues are also given.
Partially supported by NSF grant DMS 0203282.
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References
Gasper, G. and Rahman, M. (1990a). Basic Hypergeometric Series. Cambridge University Press, Cambridge.
Gasper, G. and Rahman, M. (1990b). An indefinite bibasic summation formula and some quadratic, cubic and quartic sums. Canad. J. Math., 42:1–27.
Gessel, I. and Stanton, D. (1982). Strange evaluations of hypergeometric series. SIAM J. Math. Anal., 13:295–308.
Prellberg, T. and Stanton, D. (2003). Proof of a monotonicity conjecture. J. Comb. Th. A, 103:377–381.
Rahman, M. (1989). Some cubic summation formulas for basic hypergeometric series. Utilitas Math., 36:161–172.
Rahman, M. (1993). Some quadratic and cubic summation formulas for basic hypergeometric series. Canad. J. Math., 45:394–411.
Rahman, M. (1997). Some cubic summation and transformation formulas. Ramanujan J., 1:299–308.
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© 2005 Springer Science+Business Media, Inc.
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Stanton, D. (2005). Summable Sums of Hypergeometric Series. In: Ismail, M.E., Koelink, E. (eds) Theory and Applications of Special Functions. Developments in Mathematics, vol 13. Springer, Boston, MA. https://doi.org/10.1007/0-387-24233-3_18
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DOI: https://doi.org/10.1007/0-387-24233-3_18
Publisher Name: Springer, Boston, MA
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