caa a22 4500 463178327 CHVBK 20180406164831.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s11139-006-0261-1 doi (NATIONALLICENCE)springer-10.1007/s11139-006-0261-1 Kadell Kevin Department of Mathematics and Statistics, Arizona State University, 85287-1804, Tempe, Arizona aut Telescoping partial fractions decompositions, the little q -Jacobi functions of complex order, and the nonterminating q -Saalschütz sum [Elektronische Daten] [Kevin Kadell] We use telescoping partial fractions decompositions to give new proofs of the orthogonality property and the normalization relation for the little q-Jacobi polynomials, and the q-Saalschütz sum. In [20], we followed the development [19] of Schur functions for partitions with complex parts, and we showed that there exist natural little q-Jacobi functions of complex order which satisfy extensions of the orthogonality property and normalization relation of the little q-Jacobi polynomials, and that these two results follow from and together imply the nonterminating form of the q-Saalschütz sum. Writing the q-Pochhammer symbol of complex order as a ratio of infinite products in the usual way, we obtain new telescoping partial fractions decomposition proofs of our results [20] for the little q-Jacobi functions of complex order. We give several new proofs of the q-Saalschütz sum and its nonterminating form. Springer Science + Business Media, LLC, 2006 Partial fractions decompositions nationallicence Telescoping sums nationallicence Little q -Jacobi functions nationallicence Complex order nationallicence Nonterminating q -Saalschütz sum nationallicence The Ramanujan Journal Kluwer Academic Publishers 13/1-3(2007-06-01), 449-469 1382-4090 13:1-3<449 2007 13 11139 https://doi.org/10.1007/s11139-006-0261-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-006-0261-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kadell Kevin Department of Mathematics and Statistics, Arizona State University, 85287-1804, Tempe, Arizona aut NATIONALLICENCE 773 0- The Ramanujan Journal Kluwer Academic Publishers 13/1-3(2007-06-01), 449-469 1382-4090 13:1-3<449 2007 13 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer