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

: 14

: 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.



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