Monotonicity theorems and inequalities for the complete elliptic integrals

@article{Alzer2004MonotonicityTA,
  title={Monotonicity theorems and inequalities for the complete elliptic integrals},
  author={H. Alzer and S. Qiu},
  journal={Journal of Computational and Applied Mathematics},
  year={2004},
  volume={172},
  pages={289-312}
}
  • H. Alzer, S. Qiu
  • Published 2004
  • Mathematics
  • Journal of Computational and Applied Mathematics
    • We prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind, K and E. These results lead to sharp symmetrical bounds for K and E, which improve recently discovered inequalities. 
    View via Publisher
    doi.org
    131 Citations
    Highly Influential Citations
    14
    Background Citations
    30
    Methods Citations
    1
    131 Citations
    Citation Type

    Citation Type

    Inequalities and bounds for generalized complete elliptic integrals
    • 27
    Functional Inequalities for Generalized Complete Elliptic Integrals with Two Parameters
    • Highly Influenced
    • PDF
    Inequalities and bounds for elliptic integrals
    • 31
    • PDF
    Bounds for complete elliptic integrals of the second kind with applications
    • 33
    Notes on the complete elliptic integral of the first kind
    • 23
    • PDF
    Bounds for complete elliptic integrals of the first kind
    • 24
    Monotonicity properties and inequalities for the generalized elliptic integral of the first kind
    • 5
    Monotonicity properties and inequalities related to generalized Grötzsch ring functions
    • 2
    • PDF
    Precise bounds for the weighted Hölder mean of the complete p-elliptic integrals
    • 37
    Hölder mean inequalities for the complete elliptic integrals
    • 36

    References

    SHOWING 1-10 OF 38 REFERENCES
    Sharp estimates for complete elliptic integrals
    • 38
    • Highly Influential
    Functional inequalities for complete elliptic integrals and their ratios
    • 65
    Some functional inequalities for complete elliptic integrals
    • 3
    Elliptic Integral Inequalities, with Applications
    • 27
    Functional inequalities for hypergeometric functions and complete elliptic integrals
    • 77
    • Highly Influential
    Inequalities for Means
    • 125
    • Highly Influential
    Some inequalitites for the growth of elliptic integrals
    • 13
    Sharp inequalities for the complete elliptic integral of the first kind
    • 21
    Inequalities for quasiconformal mappings in space
    • 114
    • PDF
    On certain inequalities for means, II
    • 94
    • PDF