Padé approximant related to the Wallis formula
نویسندگان
چکیده
Based on the Padé approximation method, in this paper we determine the coefficients [Formula: see text] and [Formula: see text] such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish a more accurate formula for approximating π, which refines some known results.
منابع مشابه
Padé approximant related to asymptotics for the gamma function
Based on the Padé approximation method, we determine the coefficients [Formula: see text] and [Formula: see text] ([Formula: see text]) such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish new bounds for the gamma function.
متن کاملPadé approximant related to inequalities involving the constant e and a generalized Carleman-type inequality
Based on the Padé approximation method, in this paper we determine the coefficients [Formula: see text] and [Formula: see text] ([Formula: see text]) such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish new upper bounds for [Formula: see text]. As an application, we give a generalized Carleman-type inequality.
متن کاملA Schur-Padé Algorithm for Fractional Powers of a Matrix
A new algorithm is developed for computing arbitrary real powers Ap of a matrix A ∈ Cn×n. The algorithm starts with a Schur decomposition, takes k square roots of the triangular factor T , evaluates an [m/m] Padé approximant of (1 − x)p at I − T 1/2 , and squares the result k times. The parameters k and m are chosen to minimize the cost subject to achieving double precision accuracy in the eval...
متن کاملOrthogonal polynomials and Padé approximants for reciprocal polynomial weights
Let be a closed oriented contour on the Riemann sphere. Let E and F be polynomials of degree n + 1, with zeros respectively on the positive and negative sides of . We compute the [n=n] and [n 1=n] Padé denominator at 1 to f (z) = Z 1 z t dt E (t)F (t) : As a consequence, we compute the nth orthogonal polynomial for the weight 1= (EF ). In particular, when is the unit circle, this leads to an ex...
متن کاملA Finite-Difference Time-Domain Beam-Propagation Method for TE- and TM-Wave Analyses
The application of the existing time-domain beampropagation method (TD-BPM) based on the finite-difference (FD) formula has been limited to the TE-mode analysis. To treat the TM mode as well as the TE mode, an improved TD-BPM is developed using a low-truncation-error FD formula with the aid of the alternating-direction implicit scheme. To improve the accuracy in time, a Padé (2,2) approximant i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
دوره 2017 شماره
صفحات -
تاریخ انتشار 2017