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. 
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    References

    SHOWING 1-10 OF 38 REFERENCES
    Sharp estimates for complete elliptic integrals
    • 38
    • Highly Influential
    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
    Inequalities for quasiconformal mappings in space
    • 114
    • PDF
    On certain inequalities for means, II
    • 94
    • PDF