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Padé approximants for inverse trigonometric functions and their applications [PDF]
Journal of Inequalities and Applications, 2017 The Padé approximation is a useful method for creating new inequalities and improving certain inequalities. In this paper we use the Padé approximant to give the refinements of some remarkable inequalities involving inverse trigonometric functions, it is
Shanhe Wu, Gabriel Bercu
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Bounds for Quotients of Inverse Trigonometric and Inverse Hyperbolic Functions [PDF]
Axioms, 2022 We establish new simple bounds for the quotients of inverse trigonometric and inverse hyperbolic functions such as sin−1xsinh−1x and tanh−1xtan−1x. The main results provide polynomial bounds using even quadratic functions and exponential bounds under the
Sumedh B. Thool +3 more
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Spine Surgery and Related Research, 2023 Introduction: Conventional methods for analyzing vertebral rotation are limited to postoperative patients who underwent posterior fusion. A previous methodology calculated vertebral rotation using inverse trigonometric functions based on the length of ...
Shun Okuwaki +11 more
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Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions [PDF]
Journal of Inequalities and Applications, 2016 In this paper, we present Shafer-type inequalities for inverse trigonometric functions and Gauss lemniscate functions.
Jun-Ling Sun, Chao-Ping Chen
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New Masjed Jamei–Type Inequalities for Inverse Trigonometric and Inverse Hyperbolic Functions [PDF]
Mathematics, 2022 In this paper, we establish two new inequalities of the Masjed Jamei type for inverse trigonometric and inverse hyperbolic functions and apply them to obtain some refinement and extension of Mitrinović–Adamović and Lazarević inequalities.
Ling Zhu
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Improper Integrals Involving Powers of Inverse Trigonometric and Hyperbolic Functions [PDF]
Mathematics, 2022 Three classes of improper integrals involving higher powers of arctanh, arctan, and arcsin are examined using the recursive approach. Numerous explicit formulae are established, which evaluate these integrals in terms of π, ln2, the Riemann zeta function,
Chunli Li, Wenchang Chu
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Alternating reflection method on conics leading to inverse trigonometric and hyperbolic functions
AIMS Mathematics, 2022 An unusual alternating reflection method on conics is presented to evaluate inverse trigonometric and hyperbolic functions.
François Dubeau
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Inverse Trigonometric Functions Arcsec and Arccosec [PDF]
Formalized Mathematics, 2008 The papers [1], [2], [16], [3], [12], [17], [13], [5], [8], [11], [14], [4], [6], [7], [10], [15], and [9] provide the notation and terminology for this paper. In this paper x, r denote real numbers. The following propositions are true: (1) [0, π2 [⊆ dom (the function sec). (2) ]π2 , π] ⊆ dom (the function sec). (3) [−π2 , 0[⊆ dom (the function cosec).
Bing Xie, Xiquan Liang, Fuguo Ge
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Functional inequalities for generalized inverse trigonometric and hyperbolic functions
Journal of Mathematical Analysis and Applications, 2014 Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse trigonometric and hyperbolic functions are given, as well as some Grünbaum inequalities with the aid of the classical ...
Árpád Baricz +2 more
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An Implementation of Inverse Cosine Hardware for Sound Rendering Applications [PDF]
Sensors, 2023 Sound rendering is the process of determining the sound propagation path from an audio source to a listener and generating 3D sound based on it. This task demands complex calculations, including trigonometric functions. This paper presents hardware-based
Jinyoung Lee +3 more
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