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Volumn 35, Issue 3, 2003, Pages 349-376

qMultiSum - A package for proving q-hypergeometric multiple summation identities

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EID: 0037339422     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0747-7171(02)00138-4     Document Type: Review
Times cited : (55)

References (18)
  • 1
    • 0000686589 scopus 로고
    • Generalizations and refinements of a partition theorem of Göllnitz
    • Alladi, K., Andrews, G.E., Gordon, B., 1995. Generalizations and refinements of a partition theorem of Göllnitz. J. Reine Angew. Math. 460, 165-188.
    • (1995) J. Reine Angew. Math. , vol.460 , pp. 165-188
    • Alladi, K.1    Andrews, G.E.2    Gordon, B.3
  • 2
    • 0002208328 scopus 로고    scopus 로고
    • A double bounded key identity of Göllnitz's (BIG) partition theorem
    • Garvan, F.G., Ismail, M.E.H. (Eds.), Kluwer, Dordrecht Developments in Mathematics
    • Alladi, K., Berkovich, A., 2001. A double bounded key identity of Göllnitz's (BIG) partition theorem. In: Garvan, F.G., Ismail, M.E.H. (Eds.), Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics. Developments in Mathematics, vol. 4, Kluwer, Dordrecht, pp. 13-32.
    • (2001) Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics , vol.4 , pp. 13-32
    • Alladi, K.1    Berkovich, A.2
  • 3
    • 51249165303 scopus 로고
    • Generalizations of Schur's partition theorem
    • Alladi, K., Gordon, B., 1993. Generalizations of Schur's partition theorem. Manuscripta Math. 79, 113-126.
    • (1993) Manuscripta Math. , vol.79 , pp. 113-126
    • Alladi, K.1    Gordon, B.2
  • 4
    • 0016272054 scopus 로고
    • An analytic generalization of the Rogers-Ramanujan identities for odd moduli
    • Andrews, G.E., 1974. An analytic generalization of the Rogers-Ramanujan identities for odd moduli. Proc. Natl. Acad. Sci. USA 71, 4082-4085.
    • (1974) Proc. Natl. Acad. Sci. USA , vol.71 , pp. 4082-4085
    • Andrews, G.E.1
  • 5
    • 84972580044 scopus 로고
    • Multiple series Rogers-Ramanujan type identities
    • Andrews, G.E., 1984. Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114, 267-283.
    • (1984) Pacific J. Math. , vol.114 , pp. 267-283
    • Andrews, G.E.1
  • 6
    • 0034215603 scopus 로고    scopus 로고
    • Umbral calculus, Bailey chains and pentagonal number theorems
    • Andrews, G.E., 2000. Umbral calculus, Bailey chains and pentagonal number theorems. J. Combin. Theory Ser. A 91, 464-475.
    • (2000) J. Combin. Theory Ser. A , vol.91 , pp. 464-475
    • Andrews, G.E.1
  • 7
    • 0036127628 scopus 로고    scopus 로고
    • A computer proof of a polynomial identity implying a partition theorem of Göllnitz
    • Berkovich, A., Riese, A., 2002. A computer proof of a polynomial identity implying a partition theorem of Göllnitz. Adv. Appl. Math. 28, 1-16.
    • (2002) Adv. Appl. Math. , vol.28 , pp. 1-16
    • Berkovich, A.1    Riese, A.2
  • 8
    • 0003344023 scopus 로고
    • Basic hypergeometric series
    • Rota, G.-C. (Ed.), Cambridge University Press, London and New York
    • Gasper, G., Rahman, M., 1990. Basic hypergeometric series. In: Rota, G.-C. (Ed.), Encyclopedia Math. Appl., vol. 35, Cambridge University Press, London and New York.
    • (1990) Encyclopedia Math. Appl. , vol.35
    • Gasper, G.1    Rahman, M.2
  • 10
    • 38248999979 scopus 로고
    • On Zeilberger's algorithm and its q-analogue
    • Koornwinder, T.H., 1993. On Zeilberger's algorithm and its q-analogue. J. Comput. Appl. Math. 48, 91-111.
    • (1993) J. Comput. Appl. Math. , vol.48 , pp. 91-111
    • Koornwinder, T.H.1
  • 11
    • 0031572791 scopus 로고    scopus 로고
    • 2 summation theorems for U (n) basic hypergeometric series
    • 2 summation theorems for U (n) basic hypergeometric series. Adv. Math. 131, 93-187.
    • (1997) Adv. Math. , vol.131 , pp. 93-187
    • Milne, S.C.1
  • 12
    • 46549103330 scopus 로고
    • On identities of the Rogers-Ramanujan type
    • Paule, P., 1985. On identities of the Rogers-Ramanujan type. J. Math. Anal. Appl. 107, 225-284.
    • (1985) J. Math. Anal. Appl. , vol.107 , pp. 225-284
    • Paule, P.1
  • 13
    • 0001487910 scopus 로고    scopus 로고
    • A Mathematica q-analogue of Zeilberger's algorithm based on an algebraically motivated approach to q-hypergeometric telescoping
    • Ismail, M.E.H., Masson, D.R., Rahman, M. (Eds.), Fields Inst. Commun., American Mathematical Society, Providence, RI
    • Paule, P., Riese, A., 1997. A Mathematica q-analogue of Zeilberger's algorithm based on an algebraically motivated approach to q-hypergeometric telescoping. In: Ismail, M.E.H., Masson, D.R., Rahman, M. (Eds.), Special Functions, q-Series and Related Topics. Fields Inst. Commun., 14, American Mathematical Society, Providence, RI, pp. 179-210.
    • (1997) Special Functions, Q-Series and Related Topics , vol.14 , pp. 179-210
    • Paule, P.1    Riese, A.2
  • 14
    • 0003642821 scopus 로고
    • Rekursiebetrekkingen voor lineaire hypergeometrische funkties
    • Ph.D. Thesis, Katholieke Universiteit te Leuven, Heverlee, Belgium
    • Verbaeten, P., 1976. Rekursiebetrekkingen voor lineaire hypergeometrische funkties. Ph.D. Thesis, Katholieke Universiteit te Leuven, Heverlee, Belgium.
    • (1976)
    • Verbaeten, P.1
  • 15
    • 0003197968 scopus 로고    scopus 로고
    • 50 years of Bailey's lemma
    • Betten, A. et al. (Eds.), Springer, Berlin
    • Warnaar, S.O., 2001. 50 years of Bailey's lemma. In: Betten, A. et al. (Eds.), Algebraic Combinatorics and Applications, Springer, Berlin, pp. 333-347.
    • (2001) Algebraic Combinatorics and Applications , pp. 333-347
    • Warnaar, S.O.1
  • 16
    • 0003592582 scopus 로고    scopus 로고
    • Computer generated proofs of binomial multi-sum identities
    • Diploma Thesis, RISC, J. Kepler Universität Linz, Austria
    • Wegschaider, K., 1997. Computer generated proofs of binomial multi-sum identities. Diploma Thesis, RISC, J. Kepler Universität Linz, Austria.
    • (1997)
    • Wegschaider, K.1
  • 17
    • 0001169022 scopus 로고
    • An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities
    • Wilf, H.S., Zeilberger, D., 1992. An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral identities. Invent. Math.
    • (1992) Invent. Math.
    • Wilf, H.S.1    Zeilberger, D.2
  • 18
    • 0002128111 scopus 로고
    • A fast algorithm for proving terminating hypergeometric identities
    • Zielberger, D., 1990. A fast algorithm for proving terminating hypergeometric identities. Dicrete Math. 80, 207-211.
    • (1990) Dicrete Math. , vol.80 , pp. 207-211
    • Zielberger, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.