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Table 1 Comparison of \(\pmb{\mathcal{K}(r)}\) with \(\pmb{H(r)}\) for some \(\pmb{r\in(0,1)}\)

From: Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean

r

\(\boldsymbol{\mathcal{K}(r)}\)

H ( r )

0.1

1.5747455615⋯

1.5747455614⋯

0.2

1.5868678474⋯

1.5868678471⋯

0.3

1.608048619⋯

1.608048612⋯

0.4

1.63999986⋯

1.63999977⋯

0.5

1.68575035⋯

1.68574965⋯

0.6

1.75075380⋯

1.75074958⋯

0.7

1.84569400⋯

1.84567106⋯

0.8

1.99530278⋯

1.99517293⋯