메뉴 건너뛰기




Volumn 180, Issue 1-3, 1998, Pages 3-22

q-Hypergeometric solutions of q-difference equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0009074143     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(97)00106-4     Document Type: Article
Times cited : (55)

References (19)
  • 1
    • 0042739727 scopus 로고
    • Rational solutions of linear difference and q-difference equations with polynomial coefficients
    • S.A. Abramov, Rational solutions of linear difference and q-difference equations with polynomial coefficients, Programming and Comput. Software 6 (1995) 273-278; transl. from Programmirovanie 6 (1995) 3-11.
    • (1995) Programming and Comput. Software , vol.6 , pp. 273-278
    • Abramov, S.A.1
  • 2
    • 33744951205 scopus 로고
    • transl.
    • S.A. Abramov, Rational solutions of linear difference and q-difference equations with polynomial coefficients, Programming and Comput. Software 6 (1995) 273-278; transl. from Programmirovanie 6 (1995) 3-11.
    • (1995) Programmirovanie , vol.6 , pp. 3-11
  • 3
    • 0029191776 scopus 로고
    • On polynomial solutions of linear operator equations
    • T. Levelt (Ed.), ACM Press, New York
    • S.A. Abramov, M. Bronstein, M. Petkovšek, On polynomial solutions of linear operator equations, in: T. Levelt (Ed.), Proc. ISSAC '95, ACM Press, New York, 1995, pp. 290-296.
    • (1995) Proc. ISSAC '95 , pp. 290-296
    • Abramov, S.A.1    Bronstein, M.2    Petkovšek, M.3
  • 4
    • 0040636684 scopus 로고
    • Finding all q-hypergeometric solutions of q-difference equations
    • B. Leclerc, J.-Y. Thibon (Eds.), Univ. de Marne-la-Vallée, Noisy-le-Grand
    • S.A. Abramov, M. Petkovšek, Finding all q-hypergeometric solutions of q-difference equations, in: B. Leclerc, J.-Y. Thibon (Eds.), Proc. FPSAC '95, Univ. de Marne-la-Vallée, Noisy-le-Grand, 1995, pp. 1-10.
    • (1995) Proc. FPSAC '95 , pp. 1-10
    • Abramov, S.A.1    Petkovšek, M.2
  • 6
    • 0003243481 scopus 로고
    • q-series: Their development and application in analysis, number theory, combinatorics, physics, and computer algebra
    • AMS, Providence, RI
    • G.E. Andrews, q-series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra, CBMS Regional Conference Series, No. 66, AMS, Providence, RI, 1986.
    • (1986) CBMS Regional Conference Series , vol.66
    • Andrews, G.E.1
  • 8
    • 0004107349 scopus 로고
    • Interscience Publishers, New York
    • R.M. Cohn, Difference Algebra, Interscience Publishers, New York, 1965.
    • (1965) Difference Algebra
    • Cohn, R.M.1
  • 10
    • 38248999979 scopus 로고
    • On Zeilberger's algorithm and its q-analogue: A rigorous description
    • T.H. Koornwinder, On Zeilberger's algorithm and its q-analogue: a rigorous description, J. Comput. Appl. Math. 48 (1993) 91-111.
    • (1993) J. Comput. Appl. Math. , vol.48 , pp. 91-111
    • Koornwinder, T.H.1
  • 11
    • 0002813555 scopus 로고
    • Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type
    • P. Paule, Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type. Electronic J. Combin. 1 (1994) # R10.
    • (1994) Electronic J. Combin. , vol.1
    • Paule, P.1
  • 12
    • 0000210471 scopus 로고
    • A mathematica version of Zeilberger's algorithm for proving binomial coefficient identities
    • P. Paule, M. Schorn, A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities, J. Symbolic Comput. 20 (1995) 673-698.
    • (1995) J. Symbolic Comput. , vol.20 , pp. 673-698
    • Paule, P.1    Schorn, M.2
  • 13
    • 0043025458 scopus 로고
    • Symbolic summation - Some recent developments
    • J. Fleischer, J. Grabmeier, F. Hehl, W. Küchlin (Eds.), World Scientific, Singapore
    • P. Paule, V. Strehl, Symbolic summation - some recent developments, in: Computer Algebra in Science and Engineering - Algorithms, Systems, and Applications, J. Fleischer, J. Grabmeier, F. Hehl, W. Küchlin (Eds.), World Scientific, Singapore, 1995, pp. 138-162.
    • (1995) Computer Algebra in Science and Engineering - Algorithms, Systems, and Applications , pp. 138-162
    • Paule, P.1    Strehl, V.2
  • 14
    • 0003171186 scopus 로고
    • Hypergeometric solutions of linear recurrences with polynomial coefficients
    • M. Petkovšek, Hypergeometric solutions of linear recurrences with polynomial coefficients, J. Symbolic Comput. 14 (1992) 243-264.
    • (1992) J. Symbolic Comput. , vol.14 , pp. 243-264
    • Petkovšek, M.1
  • 16
    • 0000410641 scopus 로고
    • Differentiably finite power series
    • R.P. Stanley, Differentiably finite power series, European J. Combin. 1 (1980) 175-188.
    • (1980) European J. Combin. , vol.1 , pp. 175-188
    • Stanley, R.P.1
  • 17
    • 84968468378 scopus 로고
    • Rational functions certify combinatorial identities
    • H.S. Wilf, D. Zeilberger, Rational functions certify combinatorial identities, J. Amer. Math. Soc. 3 (1990) 147-158.
    • (1990) J. Amer. Math. Soc. , vol.3 , pp. 147-158
    • Wilf, H.S.1    Zeilberger, D.2
  • 18
    • 0001169022 scopus 로고
    • An algorithmic proof theory for hypergeometric (ordinary and 'q') multisum/integral identities
    • H.S. Wilf, D. Zeilberger, An algorithmic proof theory for hypergeometric (ordinary and 'q') multisum/integral identities, Invent. Math. 108 (1992) 575-633.
    • (1992) Invent. Math. , vol.108 , pp. 575-633
    • Wilf, H.S.1    Zeilberger, D.2
  • 19
    • 0002128111 scopus 로고
    • A fast algorithm for proving terminating hypergeometric identities
    • D. Zeilberger, A fast algorithm for proving terminating hypergeometric identities, Discrete Math. 80 (1990) 207-211.
    • (1990) Discrete Math. , vol.80 , pp. 207-211
    • Zeilberger, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.