Results 11 to 20 of about 977,904 (291)
Derivative and higher-order Cauchy integral formula of matrix functions
Open Mathematics, 2021 The derivative of a nn-order matrix function on the complex field is usually defined as a n2{n}^{2}-order matrix, which is not suitable for generalizing Cauchy integral formula of matrix functions to its higher-order derivative form. In this paper, a new
Huang Xiaojie, Liu Zhixiu, Wu Chun
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Derivative formula for capacities
We obtain a derivative formula for various notions of capacity. Namely we identify the second order term in the asymptotic expansion of the capacity of a union of two sets, as their distance goes to infinity. Our result applies to the usual Newtonian capacity in the setting of random walks on the Euclidean lattice, to the family of Bessel-Riesz ...
Asselah, Amine +2 more
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Estimates For An Integral In Lp Norm Of The (N + 1)-Th Derivative Of Its Integrand [PDF]
, 2000 Basing on Taylor’s formula with an integral remaider, an integral is estimated in Lp norm of the (n + 1)-th derivative of its integrand, and the Iyengar’s inequality and many other useful inequalities are ...
Qi, Feng, Guo, Bai-Ni
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Extension of exton's hypergeometric function K16
Cubo, 2021 The purpose of this article is to introduce an extension of Exton's hypergeometric function K16 by using the extended beta function given by Özergin et al. [11].
Ahmed Ali Atash, Maisoon Ahmed Kulib
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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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Calculation of Two Types of Quaternion Step Derivatives of Elementary Functions
Mathematics, 2021 We aim to get the step derivative of a complex function, as it derives the step derivative in the imaginary direction of a real function. Given that the step derivative of a complex function cannot be derived using i, which is used to derive the step ...
Ji Eun Kim
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Some New Bounds for the Čebyšev Functional in Terms of the First Derivative and Applications [PDF]
, 2004 Some new inequalities for the Čebyšev functional in terms of the first derivative and applications for Taylor’s expansion and generalised trapezoid formula are pointed ...
Cerone, Pietro, Dragomir, Sever S
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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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Electrical Circuits RC, LC, and RLC under Generalized Type Non-Local Singular Fractional Operator
Fractal and Fractional, 2021 The current study is of interest when performing a useful extension of a crucial physical problem through a non-local singular fractional operator. We provide solutions that include three arbitrary parameters α, ρ, and γ for the Resistance-Capacitance ...
Bahar Acay, Mustafa Inc
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Fractal and Fractional, 2021 In this manuscript, the time-fractional diffusion equation in the framework of the Yang–Abdel–Cattani derivative operator is taken into account. A detailed proof for the existence, as well as the uniqueness of the solution of the time-fractional ...
Igor V. Malyk +4 more
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