Results 1 to 10 of about 13,582 (83)
Axioms, 2023 In this paper, basing on the generating function for the van der Pol numbers, utilizing the Maclaurin power series expansion and two power series expressions of a function involving the cotangent function, and by virtue of the Wronski formula and a ...
Zhen-Ying Sun, Bai-Ni Guo, Feng Qi
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On Qi’s Normalized Remainder of Maclaurin Power Series Expansion of Logarithm of Secant Function
AxiomsIn the study, the authors introduce Qi’s normalized remainder of the Maclaurin power series expansion of the function lnsecx=−lncosx; in view of a monotonicity rule for the ratio of two Maclaurin power series and by virtue of the logarithmic convexity of
Hong-Chao Zhang, Bai-Ni Guo, Wei-Shih Du
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Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function
Symmetry, 2023 In view of a general formula for higher order derivatives of the ratio of two differentiable functions, the authors establish the first form for the Maclaurin power series expansion of a logarithmic expression in term of determinants of special Hessenberg matrices whose elements involve the Bernoulli numbers.
Yue-Wu Li, Feng Qi 0001, Wei-Shih Du
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Mathematics, 2023 In the paper, by virtue of a derivative formula for the ratio of two differentiable functions and with the help of a monotonicity rule, the authors expand a logarithmic expression involving the sine function into the Maclaurin power series in terms of ...
Xin-Le Liu, Hai-Xia Long, Feng Qi
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Some Properties on Normalized Tails of Maclaurin Power Series Expansion of Exponential Function
SymmetryIn the paper, (1) in view of a general formula for any derivative of the quotient of two differentiable functions, (2) with the aid of a monotonicity rule for the quotient of two power series, (3) in light of the logarithmic convexity of an elementary function involving the exponential function, (4) with the help of an integral representation for the ...
Zhi-Hua Bao +3 more
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MathematicsIn the paper, the authors establish the monotonicity results of the ratios between normalized tails of the Maclaurin power series expansions of the sine and cosine functions and restate them in terms of the generalized hypergeometric functions.
Da-Wei Niu, Feng Qi
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Some Properties of Normalized Tails of Maclaurin Power Series Expansions of Sine and Cosine
Fractal and FractionalIn the paper, the authors introduce two notions, the normalized remainders, or say, the normalized tails, of the Maclaurin power series expansions of the sine and cosine functions, derive two integral representations of the normalized tails, prove the ...
Tao Zhang +3 more
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Open Mathematics, 2023 In this study, by virtue of a derivative formula for the ratio of two differentiable functions and with aid of a monotonicity rule, the authors expand a logarithmic expression involving the cosine function into the Maclaurin power series in terms of ...
Li Yan-Fang, Qi Feng
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Mathematics, 2023 In the existing literature, there are only two in-plane equilibrium equations for membrane problems; one does not take into account the contribution of deflection to in-plane equilibrium at all, and the other only partly takes it into account.
Jun-Yi Sun, Ji Wu, Xue Li, Xiao-Ting He
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Advances in Difference Equations, 2019 A powerful analytical approach, namely the fractional residual power series method (FRPS), is applied successfully in this work to solving a class of fractional stiff systems.
Asad Freihet +4 more
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