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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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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Turán type inequalities for generalized inverse trigonometric functions [PDF]
Filomat, 2015 In this paper we study the inverse of the eigenfunction sinp of the one-dimensional p-Laplace operator and its dependence on the parameter p, and we present a Turán type inequality for this function.
Baricz, Árpád +2 more
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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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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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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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Principal Branches of Inverse Trigonometric and Inverse Hyperbolic Functions [PDF]
ACM Communications in Computer Algebra, 2023 We discuss principal branches for five square root functions and for the inverse trigonometric and inverse hyperbolic functions. We take the standard reference in this area to be the NIST Digital Library of Mathematical Functions (DLMF). We adopt the notation for and the definitions of the principal branches of the inverse functions in the DLMF ...
Kevin M. Dempsey
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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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Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms [PDF]
SIAM Journal on Matrix Analysis and Applications, 2016 Summary: Theoretical and computational aspects of matrix inverse trigonometric and inverse hyperbolic functions are studied. Conditions for existence are given, all possible values are characterized, and the principal values acos, asin, acosh, and asinh are defined and shown to be unique primary matrix functions.
Mary Aprahamian, Nicholas J. Higham
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