منابع مشابه
Padé approximant related to the Wallis formula
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.
متن کاملPadé 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 کاملDirect application of Padé approximant for solving nonlinear differential equations
UNLABELLED This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value proble...
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 کاملBeam propagation method using a [(p- 1)/ p] Padé approximant of the propagator.
A new beam propagation method (BPM) is developed based on a direct approximation to the propagator by its [(p-1)/p] Padé approximant. The approximant is simple to construct and has the desired damping effect for the evanescent modes. The method is applied to a tapered waveguide for TM-polarized waves, based on the energy-conserving improvement of the one-way Helmholtz equation. Numerical result...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1961
ISSN: 0022-247X
DOI: 10.1016/0022-247x(61)90042-7