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Some functional inequalities for complete elliptic integrals

✍ Scribed by Andrea Laforgia; Silvana Sismondi


Book ID
112908279
Publisher
Springer Milan
Year
1992
Tongue
Italian
Weight
158 KB
Volume
41
Category
Article
ISSN
0009-725X

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## a b s t r a c t In this work, we prove that M p (K(r), E (r)) > Ο€ /2 for all r ∈ (0, 1) if and only if p β‰₯ -1/2, where M p (x, y) denotes the power mean of order p of two positive numbers x and y, and K(r) and E (r) denote the complete elliptic integrals of the first and second kinds, respectiv