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Volumn 105, Issue 1, 2004, Pages 63-77

Combinatorial proofs of Ramanujan's 1 ψ 1 summation and the q-Gauss summation

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EID: 1042279891     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcta.2003.10.002     Document Type: Article
Times cited : (24)

References (23)
  • 1
    • 0003258562 scopus 로고
    • Chapter 16 of Ramanujan's second notebook: Theta-functions and q-series
    • C. Adiga, B.C. Berndt, S. Bhargava, G.N. Watson, Chapter 16 of Ramanujan's second notebook: theta-functions and q-series, Mem. Amer. Math. Soc. 53 (315) (1985).
    • (1985) Mem. Amer. Math. Soc. , vol.53 , Issue.315
    • Adiga, C.1    Berndt, B.C.2    Bhargava, S.3    Watson, G.N.4
  • 3
    • 84968478823 scopus 로고
    • On a transformation of bilateral series with applications
    • G.E. Andrews, On a transformation of bilateral series with applications, Proc. Amer. Math. Soc. 25 (1970) 554-558.
    • (1970) Proc. Amer. Math. Soc. , vol.25 , pp. 554-558
    • Andrews, G.E.1
  • 4
    • 0002219504 scopus 로고
    • Generalized Frobenius partitions
    • G.E. Andrews, Generalized Frobenius partitions, Mem. Amer. Math. Soc. 49 (301) (1984).
    • (1984) Mem. Amer. Math. Soc. , vol.49 , Issue.301
    • Andrews, G.E.1
  • 6
    • 0001582431 scopus 로고
    • Ramanujan's extensions of the gamma and beta functions
    • R. Askey, Ramanujan's extensions of the gamma and beta functions, Amer. Math. Monthly 87 (1980) 346-359.
    • (1980) Amer. Math. Monthly , vol.87 , pp. 346-359
    • Askey, R.1
  • 8
    • 0038116320 scopus 로고    scopus 로고
    • Particle seas and basic hypergeometric series
    • S. Corteel, Particle seas and basic hypergeometric series, Adv. Appl. Math. 31 (2003) 199-214.
    • (2003) Adv. Appl. Math. , vol.31 , pp. 199-214
    • Corteel, S.1
  • 12
    • 0002452730 scopus 로고
    • Über die Charaktere der symmetrischen Gruppe
    • G. Frobenius, Über die Charaktere der symmetrischen Gruppe, Sitzber. Preuss. Akad., Berlin, 1900, 516-534.
    • (1900) Sitzber. Preuss. Akad., Berlin , pp. 516-534
    • Frobenius, G.1
  • 14
    • 0000243146 scopus 로고
    • Beiträge zur Theorie der Heineschen Reihen
    • W. Hahn, Beiträge zur Theorie der Heineschen Reihen, Math. Nachr. 2 (1949) 340-379.
    • (1949) Math. Nachr. , vol.2 , pp. 340-379
    • Hahn, W.1
  • 15
    • 85030905405 scopus 로고    scopus 로고
    • Ramanujan, reprinted, American Mathematical Society, Chelsea, Providence, RI
    • G.H. Hardy, Ramanujan, reprinted, American Mathematical Society, Chelsea, Providence, RI, 1999.
    • (1999)
    • Hardy, G.H.1
  • 19
    • 84972554387 scopus 로고
    • Bijective proofs of basic hypergeometric series identities
    • J.T. Joichi, D. Stanton, Bijective proofs of basic hypergeometric series identities, Pacific J. Math. 127 (1987) 103-120.
    • (1987) Pacific J. Math. , vol.127 , pp. 103-120
    • Joichi, J.T.1    Stanton, D.2
  • 20
    • 1042283039 scopus 로고
    • A proof of Ramanujan's identity by use of loop integral
    • K. Mimachi, A proof of Ramanujan's identity by use of loop integral, SIAM J. Math. Anal. 19 (1988) 1490-1493.
    • (1988) SIAM J. Math. Anal. , vol.19 , pp. 1490-1493
    • Mimachi, K.1
  • 21
    • 85030900859 scopus 로고    scopus 로고
    • Partition bijections
    • to appear
    • I. Pak, Partition bijections, Ramanujan J., to appear.
    • Ramanujan J.
    • Pak, I.1
  • 22
    • 84963057188 scopus 로고
    • An enumerative proof of an identity of Jacobi
    • E.M. Wright, An enumerative proof of an identity of Jacobi, J. London Math. Soc. 40 (1965) 55-57.
    • (1965) J. London Math. Soc. , vol.40 , pp. 55-57
    • Wright, E.M.1
  • 23
    • 0038029943 scopus 로고    scopus 로고
    • Combinatorial proofs of generating function identities for F-partitions
    • A.J. Yee, Combinatorial proofs of generating function identities for F-partitions, J. Combin. Theory Ser. A 102 (2003) 217-228.
    • (2003) J. Combin. Theory Ser. A , vol.102 , pp. 217-228
    • Yee, A.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.