메뉴 건너뛰기




Volumn 146, Issue 2, 2007, Pages 212-226

Inequalities and bounds for elliptic integrals

Author keywords

Convexity; Inequalities; Legendre's elliptic integrals; Means; Symmetric elliptic integrals; The R hypergeometric functions

Indexed keywords


EID: 34249097797     PISSN: 00219045     EISSN: 10960430     Source Type: Journal    
DOI: 10.1016/j.jat.2006.12.004     Document Type: Article
Times cited : (33)

References (32)
  • 1
    • 5044237360 scopus 로고    scopus 로고
    • Monotonicity theorems and inequalities for the complete elliptic integrals
    • Alzer H.L., and Qiu S.-L. Monotonicity theorems and inequalities for the complete elliptic integrals. J. Comput. Appl. Math. 172 (2004) 289-312
    • (2004) J. Comput. Appl. Math. , vol.172 , pp. 289-312
    • Alzer, H.L.1    Qiu, S.-L.2
  • 4
    • 0001356663 scopus 로고
    • Functional inequalities for complete elliptic integrals and their ratios
    • Anderson G.D., Vamanamurthy M.K., and Vuorinen M. Functional inequalities for complete elliptic integrals and their ratios. SIAM J. Math. Anal. 21 (1990) 536-549
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 536-549
    • Anderson, G.D.1    Vamanamurthy, M.K.2    Vuorinen, M.3
  • 5
    • 0010990458 scopus 로고
    • Functional inequalities for hypergeometric functions and complete elliptic integrals
    • Anderson G.D., Vamanamurthy M.K., and Vuorinen M. Functional inequalities for hypergeometric functions and complete elliptic integrals. SIAM J. Math. Anal. 31 (1992) 512-524
    • (1992) SIAM J. Math. Anal. , vol.31 , pp. 512-524
    • Anderson, G.D.1    Vamanamurthy, M.K.2    Vuorinen, M.3
  • 6
    • 0010966012 scopus 로고
    • Hypergeometric functions and elliptic integrals
    • Srivastava H.M., and Owa S. (Eds), World Scientific, Singapore
    • Anderson G.D., Vamanamurthy M.K., and Vuorinen M. Hypergeometric functions and elliptic integrals. In: Srivastava H.M., and Owa S. (Eds). Current Topics in Analytic Function Theory (1992), World Scientific, Singapore 48-85
    • (1992) Current Topics in Analytic Function Theory , pp. 48-85
    • Anderson, G.D.1    Vamanamurthy, M.K.2    Vuorinen, M.3
  • 8
    • 0041152123 scopus 로고    scopus 로고
    • An inequality involving the generalized hypergeometric function and the arc length of an ellipse
    • Barnard R.W., Pearce K., and Richards K.C. An inequality involving the generalized hypergeometric function and the arc length of an ellipse. SIAM J. Math. Anal. 31 (2000) 693-699
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 693-699
    • Barnard, R.W.1    Pearce, K.2    Richards, K.C.3
  • 9
    • 0034550890 scopus 로고    scopus 로고
    • 2 and comparisons of the classical approximations of elliptical arc length
    • 2 and comparisons of the classical approximations of elliptical arc length. SIAM J. Math. Anal. 32 (2000) 403-419
    • (2000) SIAM J. Math. Anal. , vol.32 , pp. 403-419
    • Barnard, R.W.1    Pearce, K.2    Richards, K.C.3
  • 10
    • 0000318819 scopus 로고
    • Inequalities for compound mean iterations with logarithmic asymptotes
    • Borwein J.M., and Borwein P.B. Inequalities for compound mean iterations with logarithmic asymptotes. J. Math. Anal. Appl. 177 (1993) 572-582
    • (1993) J. Math. Anal. Appl. , vol.177 , pp. 572-582
    • Borwein, J.M.1    Borwein, P.B.2
  • 11
    • 0037815588 scopus 로고
    • Some series and bounds for incomplete elliptic integrals
    • Carlson B.C. Some series and bounds for incomplete elliptic integrals. J. Math. Phys. 40 (1961) 125-134
    • (1961) J. Math. Phys. , vol.40 , pp. 125-134
    • Carlson, B.C.1
  • 12
    • 84966250852 scopus 로고
    • Some inequalities for hypergeometric functions
    • Carlson B.C. Some inequalities for hypergeometric functions. Proc. Amer. Math. Soc. 17 (1966) 32-39
    • (1966) Proc. Amer. Math. Soc. , vol.17 , pp. 32-39
    • Carlson, B.C.1
  • 13
    • 84968514100 scopus 로고
    • Inequalities for a symmetric elliptic integral
    • Carlson B.C. Inequalities for a symmetric elliptic integral. Proc. Amer. Math. Soc. 25 (1970) 698-703
    • (1970) Proc. Amer. Math. Soc. , vol.25 , pp. 698-703
    • Carlson, B.C.1
  • 14
    • 0001583559 scopus 로고
    • Algorithms involving arithmetic and geometric means
    • Carlson B.C. Algorithms involving arithmetic and geometric means. Amer. Math. Monthly 78 (1971) 496-505
    • (1971) Amer. Math. Monthly , vol.78 , pp. 496-505
    • Carlson, B.C.1
  • 16
    • 0012173224 scopus 로고
    • Numerical computation of real or complex elliptic integrals
    • Carlson B.C. Numerical computation of real or complex elliptic integrals. Numer. Algorithms 10 (1995) 13-26
    • (1995) Numer. Algorithms , vol.10 , pp. 13-26
    • Carlson, B.C.1
  • 17
    • 0000825250 scopus 로고
    • Asymptotic expansions of the first elliptic integral
    • Carlson B.C., and Gustafson J.L. Asymptotic expansions of the first elliptic integral. SIAM J. Math. Anal. 16 (1985) 1072-1092
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 1072-1092
    • Carlson, B.C.1    Gustafson, J.L.2
  • 18
    • 21344499241 scopus 로고
    • Asymptotics approximations for symmetric elliptic integrals
    • Carlson B.C., and Gustafson J.L. Asymptotics approximations for symmetric elliptic integrals. SIAM J. Math. Anal. 25 (1994) 288-303
    • (1994) SIAM J. Math. Anal. , vol.25 , pp. 288-303
    • Carlson, B.C.1    Gustafson, J.L.2
  • 19
    • 17844406470 scopus 로고
    • An inequality of the AGM and the logarithmic mean
    • Carlson B.C., and Vuorinen M. An inequality of the AGM and the logarithmic mean. SIAM Rev. 33 (1991) 655
    • (1991) SIAM Rev. , vol.33 , pp. 655
    • Carlson, B.C.1    Vuorinen, M.2
  • 20
    • 34249060498 scopus 로고    scopus 로고
    • J.L. Gustafson, Asymptotic formulas for elliptic integrals, Ph.D. Thesis, Iowa State University, Ames, IA, 1982.
  • 21
    • 0034347312 scopus 로고    scopus 로고
    • Asymptotic expansions of standard elliptic integrals
    • López J.L. Asymptotic expansions of standard elliptic integrals. SIAM J. Math. Anal. 31 (2000) 754-775
    • (2000) SIAM J. Math. Anal. , vol.31 , pp. 754-775
    • López, J.L.1
  • 22
    • 0035648223 scopus 로고    scopus 로고
    • Uniform asymptotic expansions of symmetric elliptic integrals
    • López J.L. Uniform asymptotic expansions of symmetric elliptic integrals. Constr. Approx. 17 (2001) 535-559
    • (2001) Constr. Approx. , vol.17 , pp. 535-559
    • López, J.L.1
  • 23
    • 0038347887 scopus 로고    scopus 로고
    • Bounds for symmetric elliptic integrals
    • Neuman E. Bounds for symmetric elliptic integrals. J. Approx. Theory 122 (2003) 249-259
    • (2003) J. Approx. Theory , vol.122 , pp. 249-259
    • Neuman, E.1
  • 24
    • 34249087622 scopus 로고    scopus 로고
    • E. Neuman, On Gauss lemniscate functions and lemniscatic mean, submitted for publication.
  • 25
    • 1342276621 scopus 로고    scopus 로고
    • On certain means of two arguments and their extensions
    • Neuman E., and Sándor J. On certain means of two arguments and their extensions. Internat. J. Math. Math. Sci. 16 (2003) 981-993
    • (2003) Internat. J. Math. Math. Sci. , vol.16 , pp. 981-993
    • Neuman, E.1    Sándor, J.2
  • 26
    • 33646403482 scopus 로고    scopus 로고
    • On the Schwab-Borchardt mean II
    • Neuman E., and Sándor J. On the Schwab-Borchardt mean II. Math. Pannon. 17 (2006) 49-59
    • (2006) Math. Pannon. , vol.17 , pp. 49-59
    • Neuman, E.1    Sándor, J.2
  • 29
    • 0030536809 scopus 로고    scopus 로고
    • Sharp estimates for complete elliptic integrals
    • Qiu S.-L., and Vamanamurthy M.K. Sharp estimates for complete elliptic integrals. SIAM J. Math. Anal. 27 (1996) 823-834
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 823-834
    • Qiu, S.-L.1    Vamanamurthy, M.K.2
  • 32
    • 84966239680 scopus 로고
    • Symmetric elliptic integrals of the third kind
    • Zill D.G., and Carlson B.C. Symmetric elliptic integrals of the third kind. Math. Comput. 24 (1970) 199-214
    • (1970) Math. Comput. , vol.24 , pp. 199-214
    • Zill, D.G.1    Carlson, B.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.