Sharp approximations for the complete elliptic integrals of the second kind by one-parameter means

A new chain of inequalities involving the Toader-Qi, logarithmic and exponential means

“…Such type power series appear frequently in certain special functions. A similar signs rule was proven in [36,39] and plays a key role in the study of means and special functions, see for example, [21,28,31,34,37,43].…”

A Rational Approximation for the Complete Elliptic Integral of the First Kind

“…To prove Theorem 1, we need a sign rule for a type of special power series and polynomials, which has been proven in [9,15,16] by Yang et al It should be noted that this sign rule plays an important role in the study for certain special functions, see, for example, [17][18][19][20][21].…”

Sharp inequalities for Toader mean in terms of other bivariate means

“…There are many bounds for the Toader mean in terms of various elementary means, see for example, [6,7,[9][10][11][12][13][14][15]17,[22][23][24][25][26][27][28], and recent papers [16,[29][30][31][32]. In particular, we mention here several interesting results.…”