Results 1 to 10 of about 6,682 (102)

Determinantal Expressions, Identities, Concavity, Maclaurin Power Series Expansions for van der Pol Numbers, Bernoulli Numbers, and Cotangent

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

Axioms
In 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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Some Properties of Normalized Tails of Maclaurin Power Series Expansions of Sine and Cosine

Fractal and Fractional
In 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, Zhen-Hang Yang, Feng Qi, Wei-Shih Du   +3 more
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Monotonicity Results of Ratios between Normalized Tails of Maclaurin Power Series Expansions of Sine and Cosine

Mathematics
In 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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Designing novel LDO voltage regulator implementation on FPGA using neural network [PDF]

Journal of Applied Research on Industrial Engineering, 2021
This paper describes a new technique for implementing an Artificial Neural Network (ANN) using Field Programmable Gate Array (FPGA). The goal is design the Low Drop Output (LDO) voltage-regulator circuit with the desired features depending on the ...
Mahdieh Jahangiri, Ali Farrokhi, Amir Amirabadi   +2 more
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An Exact In-Plane Equilibrium Equation for Transversely Loaded Large Deflection Membranes and Its Application to the Föppl-Hencky Membrane Problem

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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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, Wei-Shih Du
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MacLaurin’s series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions, closed-form formula of specific partial Bell polynomials, and series representation of generalized logsine function

Applicable Analysis and Discrete Mathematics, 2022
In the paper, the authors find series expansions and identities for positive integer powers of inverse (hyperbolic) sine and tangent, for composite of incomplete gamma function with inverse hyperbolic sine, in terms of the first kind Stirling numbers, apply a newly established series expansion to derive a closed-form formula for specific ...
Bai-Ni Guo, Dongkyu Lim, Feng Qi
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Maclaurin's series expansions of real powers of inverse (hyperbolic) cosine functions and applications [PDF]

, 2021
Abstract In the paper, by means of the Faa di Bruno formula, with the help of explicit formulas for special values of the Bell polynomials of the second kind with respect to a specific sequence, and by virtue of two combinatorial identities containing the Stirling numbers of the first kind, the author establishes Maclaurin's series expansions ...
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A Series Expansion of a Logarithmic Expression and a Decreasing Property of the Ratio of Two Logarithmic Expressions Containing Sine

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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