Some inequalities for the growth of elliptic integrals



: Qiu S., Vamanamurthy M., Vuorinen M.

: 1998

 SIAM Journal on Mathematical Analysis

: SIAM Journal on Mathematical Analysis

: 29

: 5

: 1224

: 1237

: 0036-1410

: http://api.elsevier.com/content/abstract/scopus_id:0032335743


Growth of the complete elliptic integral K(r) near the singularity r = 1 is studied and new bounds in terms of elementary functions are obtained. In particular, two recent conjectures are solved and various convexity properties of K(r) are given.


Concave, Convex, Elliptic integrals, Modulus, Ring



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