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Articles

Some properties of the generalized Jacobian elliptic functions III

Pages 824-834 | Received 02 Feb 2016, Accepted 24 Jun 2016, Published online: 17 Jul 2016

References

  • Lawden DF. Elliptic functions and applications. Applied Mathematics Series, Vol. 80. New York: Springer-Verlag; 1989.
  • Carlson BC. Special functions of applied mathematics. New York: Academic Press; 1977.
  • Neville EM. Jacobian elliptic functions. 2nd ed. London: Oxford Univ. Press; 1951.
  • Olver FWJ, Lozier DW, Boisvert RF, Clark CW, editors. NIST handbook of mathematical functions. New York: Cambridge University Press; 2010.
  • Whittaker ET, Watson GN. A course of modern analysis. 4th ed. New York: Cambridge University Press; 1990.
  • Takeuchi S. Generalized Jacobian elliptic functions and their application to bifurcation problems associated with p-Laplacian. J Math Anal Appl. 2012;385:24–35. doi: 10.1016/j.jmaa.2011.06.063
  • Neuman E. Inequalities for the generalized trigonometric, hyperbolic and Jacobian elliptic functions. J Math Inequal. 2015;7:709–726. doi: 10.7153/jmi-09-59
  • Neuman E. One- and two-sided inequalities for Jacobian elliptic functions and related results. Integral Transforms Spec Funct. 2010;21:399–407. doi: 10.1080/10652460903345961
  • Neuman E. Inequalities for Jacobian elliptic functions and Gauss lemniscate functions. Appl Math Comput. 2012;218:7774–7782.
  • Neuman E. Product formulas and bounds for Jacobian elliptic functions with applications. Integral Transforms Spec Funct. 2012;23:347–354. doi: 10.1080/10652469.2011.590807
  • Neuman E. Wilker and Huygens-type inequalities for the generalized trigonometric and for the generalized hyperbolic functions. Appl Math Comput. 2014;230:211–217.
  • Neuman E. Inequalities involving generalized Jacobian elliptic functions. Integral Transforms Spec Funct. 2014;25:864–873. doi: 10.1080/10652469.2014.937434
  • Neuman E. Some properties of the generalized Jacobian elliptic functions. Integral Transforms Spec Funct. 2015;26:498–506. doi: 10.1080/10652469.2015.1020485
  • Takeuchi S. The basis property of generalized Jacobian elliptic functions. arXiv. 2013: 130.0597v1: Oct. 2013.
  • Neuman E. Some properties of the generalized Jacobian elliptic functions II. Integral Transforms Spec Funct. 2016;27:101–110. doi: 10.1080/10652469.2015.1098634
  • Niculescu CP. Convexity according to the geometric mean. Math Inequal Appl. 2000;3:155–167.
  • Neuman E, Sándor J. Inequalities involving Jacobian elliptic functions and their inverses. Integral Transforms Spec Funct. 2012;23:719–722. doi: 10.1080/10652469.2011.627561
  • Neuman E. Two-sided inequalities for the lemniscate functions. J Inequal Spec Funct. 2010;1:1–7.
  • Neuman E. On Wilker and Huygens-type inequalities. Math Inequal Appl. 2012;15:271–279.
  • Neuman E. Inequalities for weighted sums of powers and their applications. Math Inequal Appl. 2012;15:995–1005.
  • Carlson BC. Some inequalities for hypergeometric functions. Proc Amer Math Soc. 1968;17:32–39. doi: 10.1090/S0002-9939-1966-0188497-6
  • Neuman E. Wilker- and Huygens-type inequalities for Jacobian elliptic and theta functions. Integral Transforms Spec Funct. 2014;25:240–248. doi: 10.1080/10652469.2013.838761
  • Van der Corput JG. Problem 95. Wisk Opgaven. 1935;16:242–243.
  • Baricz A, Laforgia A, Pogány TK. Van der Corput inequalities for Bessel functions. Integral Transforms Spec Funct. 2015;26:78–87. doi: 10.1080/10652469.2014.975419
  • Lindqvist P. Some remarkable sine and cosine functions. Ricerche Mat. 1995;44(2):269–290.
  • Klén R, Vuorinen M, Zhang X. Inequalities for the generalized trigonometric and hyperbolic functions. J Math Anal Appl. 2014;409:521–529. doi: 10.1016/j.jmaa.2013.07.021
  • Neuman E. A note on the Jacobian elliptic sine function. Integral Transforms Spec Funct. 2013;24:548–553. doi: 10.1080/10652469.2012.720254

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