Derivatives of tangent function and tangent numbers
, 2015 In the paper, by induction, the Fa\`a di Bruno formula, and some techniques in the theory of complex functions, the author finds explicit formulas for higher order derivatives of the tangent and cotangent functions as well as powers of the sine and ...
Bourbaki +37 more
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Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach. [PDF]
Heliyon, 2023 Mahmood A +6 more
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The asymptotic expansion of a generalisation of the Euler-Jacobi series [PDF]
, 2015 We consider the asymptotic expansion of the sum Sp(a; w) = ∞Ʃ n=1 e−anp/nw as a → 0 in | arg a| <1/2π for arbitrary finite p > 0 and w > 0. Our attention is concentrated mainly on the case when p and w are both even integers, where the expansion
Paris, Richard B.
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On some determinants involving the tangent function
, 2019 Let $p$ be an odd prime and let $a,b\in\mathbb Z$ with $p\nmid ab$. In this paper we mainly evaluate $$T_p^{(\delta)}(a,b):=\det\left[\tan\pi\frac{aj^2+bk^2}p\right]_{\delta\le j,k\le (p-1)/2}\ \ (\delta=0,1).$$ For example, in the case $p\equiv3\pmod4 ...
Sun, Zhi-Wei
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Coefficient estimates for some classes of functions associated with \(q\)-function theory
, 2017 In this paper, for every $q\in(0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach type problem for the class of $q$-convex functions of order $\alpha, 0\le ...
Agrawal, Sarita
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Some implications of a new definition of the exponential function on time scales
, 2010 We present a new approach to exponential functions on time scales and to timescale analogues of ordinary differential equations. We describe in detail the Cayley-exponential function and associated trigonometric and hyperbolic functions. We show that the
Cieśliński, Jan L.
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APP accumulates with presynaptic proteins around amyloid plaques: A role for presynaptic mechanisms in Alzheimer's disease? [PDF]
Alzheimers Dement, 2022 Jordà-Siquier T +8 more
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New approximation inequalities for circular functions. [PDF]
J Inequal Appl, 2018 Zhu L, Nenezić M.
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Refinements and generalizations of some inequalities of Shafer-Fink's type for the inverse sine function. [PDF]
J Inequal Appl, 2017 Malešević B, Rašajski M, Lutovac T.
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