AbstractIn this note by using some elementary computations we present some new sharp lower and upper bounds for the complete elliptic integrals of the first kind. These results improve some known bounds in the literature and are deduced from the well-known Wallis inequality, which has been studied extensively in the last 10 years
This is a survey and expository article. Some new developments on refinements, generalizations, and ...
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new ...
In this article we give evaluations of the two complete elliptic in-tegrals K and E in the form of R...
AbstractComputable lower and upper bounds for the symmetric elliptic integrals and for Legendre's in...
Abstract In this paper, we show an elegant inequality involving the ratio of generalized complete el...
Let K(r) be the complete elliptic integral of the first kind. Then, the inequality 2K(r)/π>tanh−1(r)...
AbstractComputable bounds for the generalized complete elliptic integrals of the first and second ki...
In this paper, we obtain a new simple rational approximation for Ka(r): the inequality 2Ka(r)/π>g2r′...
AbstractWe prove monotonicity properties of certain combinations of complete elliptic integrals of t...
Abstract. This is a survey and expository article. Some new developments on refinements, generalizat...
One of the most important applications of elliptic integrals in engineering mathematics is their usa...
This is an expository article. Some developments on refinements,\ud generalizations, applications of...
AbstractIn this paper, we establish a necessary and sufficient condition for the convexity of the co...
Abstract We generalize several monotonicity and convexity properties as well as sharp inequalities f...
In this paper, we obtain a concise high-precision approximation for $ \mathcal{K}(r) $: $ \begin...
This is a survey and expository article. Some new developments on refinements, generalizations, and ...
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new ...
In this article we give evaluations of the two complete elliptic in-tegrals K and E in the form of R...
AbstractComputable lower and upper bounds for the symmetric elliptic integrals and for Legendre's in...
Abstract In this paper, we show an elegant inequality involving the ratio of generalized complete el...
Let K(r) be the complete elliptic integral of the first kind. Then, the inequality 2K(r)/π>tanh−1(r)...
AbstractComputable bounds for the generalized complete elliptic integrals of the first and second ki...
In this paper, we obtain a new simple rational approximation for Ka(r): the inequality 2Ka(r)/π>g2r′...
AbstractWe prove monotonicity properties of certain combinations of complete elliptic integrals of t...
Abstract. This is a survey and expository article. Some new developments on refinements, generalizat...
One of the most important applications of elliptic integrals in engineering mathematics is their usa...
This is an expository article. Some developments on refinements,\ud generalizations, applications of...
AbstractIn this paper, we establish a necessary and sufficient condition for the convexity of the co...
Abstract We generalize several monotonicity and convexity properties as well as sharp inequalities f...
In this paper, we obtain a concise high-precision approximation for $ \mathcal{K}(r) $: $ \begin...
This is a survey and expository article. Some new developments on refinements, generalizations, and ...
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new ...
In this article we give evaluations of the two complete elliptic in-tegrals K and E in the form of R...
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