Abstract
In this paper, we provide some new continued fraction approximation and inequalities of the Somos quadratic recurrence constant, using its relation with the generalized Euler constant.
Highlights
Somos [ ] defined the sequence gn = ngn, with g = in
(n → ∞), where the constant σ = . . . . is known as the Somos quadratic recurrence constant. This constant appears in important problems by pure representations, σ=
In order to deduce some estimates for the σ constant, we evaluate the series
Summary
. is known as the Somos quadratic recurrence constant. Sondow and Hadjicostas [ ] defined the generalized Somos quadratic recurrence constant, by t /(t– ). Σ these functions are closely related to the Somos quadratic recurrence constant σ. Many inspiring results of establishing more precise inequalities and more accurate approximations for the Somos quadratic recurrence constant and generalized-Eulerconstant function were given. Lu and Song [ ] gave sharper bounds Motivated by this important work, in this paper we will continue our previous work [ – ] and apply a multiple-correction method to construct some new sharper double inequality of the error estimate for the Somos quadratic recurrence constant. Proof Based on our previous work we will apply multiple-correction method and study the double inequality of the error estimate as follows.
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