Document Zbl 0573.33001

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Anderson, G. D.; Vamanamurthy, M. K.

Inequalities for elliptic integrals. (English) Zbl 0573.33001

Publ. Inst. Math., Nouv. Sér. 37(51), 61-63 (1985).

Sharp lower and upper estimates are obtained for five expressions involving complete elliptic integrals of the first and second kind. The proofs for four of these are elementary, while the last involves contour integration and some inequalities for elliptic functions.

Cited in 4 Documents

MSC:

33E05

Elliptic functions and integrals

Keywords:

complete elliptic integrals; inequalities for elliptic functions

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Digital Library of Mathematical Functions:

§19.9(i) Complete Integrals ‣ §19.9 Inequalities ‣ Legendre’s Integrals ‣ Chapter 19 Elliptic Integrals