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Volumn 18, Issue 1, 2009, Pages 91-102

A formula for a quartic integral: A survey of old proofs and some new ones

Author keywords

Integrals; Landen transformations; Rational integrals; WZ method

Indexed keywords


EID: 58649124545     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11139-007-9041-9     Document Type: Article
Times cited : (31)

References (17)
  • 2
    • 0032615536 scopus 로고    scopus 로고
    • An integral hidden in Gradshteyn and Ryzhik
    • G. Boros V. Moll 1999 An integral hidden in Gradshteyn and Ryzhik J. Comput. Appl. Math. 106 361 368
    • (1999) J. Comput. Appl. Math. , vol.106 , pp. 361-368
    • Boros, G.1    Moll, V.2
  • 3
    • 0002885212 scopus 로고    scopus 로고
    • A rational Landen transformation. the case of degree 6
    • Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis American Mathematical Society Providence
    • Boros, G., Moll, V.: A rational Landen transformation. The case of degree 6. In: Knopp, G., Mendoza, E.T., Quinto, E.L., Grinberg, S., Berhanu, M. (eds.) Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis. Contemporary Mathematics, vol. 251, pp. 83-89. American Mathematical Society, Providence (2000)
    • (2000) Contemporary Mathematics , vol.251 , pp. 83-89
    • Boros, G.1    Moll, V.2    Knopp, G.3    Mendoza, E.T.4    Quinto, E.L.5    Grinberg, S.6    Berhanu, M.7
  • 4
    • 0035338061 scopus 로고    scopus 로고
    • The double square root, Jacobi polynomials and Ramanujan's master theorem
    • G. Boros V. Moll 2001 The double square root, Jacobi polynomials and Ramanujan's master theorem J. Comput. Appl. Math. 130 337 344
    • (2001) J. Comput. Appl. Math. , vol.130 , pp. 337-344
    • Boros, G.1    Moll, V.2
  • 5
    • 0036013526 scopus 로고    scopus 로고
    • Landen transformation and the integration of rational functions
    • G. Boros V. Moll 2001 Landen transformation and the integration of rational functions Math. Comput. 71 649 668
    • (2001) Math. Comput. , vol.71 , pp. 649-668
    • Boros, G.1    Moll, V.2
  • 7
    • 58649085644 scopus 로고    scopus 로고
    • An elementary evaluation of a quartic integral
    • G. Boros V. Moll S. Riley 2005 An elementary evaluation of a quartic integral Scientia 11 1 12
    • (2005) Scientia , vol.11 , pp. 1-12
    • Boros, G.1    Moll, V.2    Riley, S.3
  • 9
    • 0004616128 scopus 로고
    • Gauss and the arithmetic-geometric mean
    • D. Cox 1985 Gauss and the arithmetic-geometric mean Notices AMS 32 147 151
    • (1985) Notices AMS , vol.32 , pp. 147-151
    • Cox, D.1
  • 10
    • 11844281268 scopus 로고    scopus 로고
    • Review of irresistible integrals: Symbolics, analysis and experiments in the evaluation of integrals, by George Boros and Victor H. Moll
    • J.J. Foncannon 2006 Review of irresistible integrals: symbolics, analysis and experiments in the evaluation of integrals, by George Boros and Victor H. Moll Math. Intel. 28 65 68
    • (2006) Math. Intel. , vol.28 , pp. 65-68
    • Foncannon, J.J.1
  • 13
    • 0038116787 scopus 로고    scopus 로고
    • A geometric view of rational Landen transformation
    • J. Hubbard V. Moll 2003 A geometric view of rational Landen transformation Bull. Lond. Math. Soc. 35 293 301
    • (2003) Bull. Lond. Math. Soc. , vol.35 , pp. 293-301
    • Hubbard, J.1    Moll, V.2
  • 14
    • 38849084530 scopus 로고    scopus 로고
    • Rational Landen transformations on ℝ
    • D. Manna V. Moll 2007 Rational Landen transformations on ℝ Math. Comput. 76 2023 2043
    • (2007) Math. Comput. , vol.76 , pp. 2023-2043
    • Manna, D.1    Moll, V.2
  • 15
    • 34147158853 scopus 로고    scopus 로고
    • A simple example of a new class of Landen transformations
    • D. Manna V. Moll 2007 A simple example of a new class of Landen transformations Am. Math. Mon. 114 232 241
    • (2007) Am. Math. Mon. , vol.114 , pp. 232-241
    • Manna, D.1    Moll, V.2
  • 17
    • 58649093255 scopus 로고    scopus 로고
    • Petkovsek, M., Wilf, H., Zeilberger, D.: A=B, 1st edn. A.K. Peters (1996)
    • Petkovsek, M., Wilf, H., Zeilberger, D.: A=B, 1st edn. A.K. Peters (1996)


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.