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 Mathematic...
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This paper studies eight families of infinite series involving hyperbolic functions. Under some conditions, these series are linear combinations of derivatives of Eisenstein series. Using complex multiplication theory...
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This paper studies eight families of infinite series involving hyperbolic functions. Under some conditions, these series are linear combinations of derivatives of Eisenstein series. Using complex multiplication theory, the structure of the rings of modular forms and quasimodular forms, and certain differential operators defined on these rings, this paper gives a systematic method for computing the values of these series at CM points. This paper also expresses the generalized reciprocal sums of Fibonacci numbers as the special values of the series mentioned above. Thus it gives some algebraic independence results about the generalized reciprocal sums of Fibonacci numbers. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Using classical analytic techniques, the Wilker-Anglesio inequality and parameterized Wilker inequality for hyperbolic functions are proved. The main result is then applied to deriving a hyperbolic analogue of the San...
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Using classical analytic techniques, the Wilker-Anglesio inequality and parameterized Wilker inequality for hyperbolic functions are proved. The main result is then applied to deriving a hyperbolic analogue of the Sandor-Bencze inequality. (C) 2011 Published by Elsevier Ltd
In the current paper, Galilean relativism with coupled parameters is discussed, which, in the special case of non-relativistic conditions, transitions into the well-known Galilean relativity. The extension of the prin...
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In the current paper, Galilean relativism with coupled parameters is discussed, which, in the special case of non-relativistic conditions, transitions into the well-known Galilean relativity. The extension of the principles of Galilean relativity is considered, which includes the application of proper time and proper coordinates, connected through a hyperbolic function of rapidity. Relativistic Galilean coordinates have been obtained. The results show that the proper relativistic Galilean coordinates are invariant under Lorentz transformations with respect to the proper Galilean interval. An extension of the Jacobi theorem, formulated by Einstein for dynamic functions with coupled parameters, is presented in the form of the Jacobi-Milekhin theorem. Invariants with respect to the proper coordinates have been derived from the Jacobi equation. The motion of a relativistic particle is demonstrated through the Galilean and Lorentz coordinates in a one-dimensional laser pulse with linear polarization.
It is well known that the correlation between financial products or financial institutions, e.g. plays an essential role in pricing and evaluation of financial derivatives. Using simply a constant or deterministic cor...
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It is well known that the correlation between financial products or financial institutions, e.g. plays an essential role in pricing and evaluation of financial derivatives. Using simply a constant or deterministic correlation may lead to correlation risk, since market observations give evidence that correlation is not a deterministic quantity. In this work, we propose a new approach to model the correlation as a hyperbolic function of a stochastic process. Our general approach provides a stochastic correlation which is much more realistic to model real- world phenomena and could be used in many financial application fields. Furthermore, it is very flexible: any mean-reverting process (with positive and negative values) can be regarded and no additional parameter restrictions appear which simplifies the calibration procedure. As an example, we compute the price of a Quanto applying our new approach. Using our numerical results we discuss concisely the effect of considering stochastic correlation on pricing the Quanto.
In this paper, an unity of Mitrinovic-Adamovic and Cusa-Huygens inequalities for circular functions is established, and the analogue one of Lazarevic and Cusa-Huygens-type inequalities for hyperbolic functions is pres...
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In this paper, an unity of Mitrinovic-Adamovic and Cusa-Huygens inequalities for circular functions is established, and the analogue one of Lazarevic and Cusa-Huygens-type inequalities for hyperbolic functions is presented. At the same time, the new inequality for circular functions is extended to another interval.
Bernoulli and Euler polynomials are considered for large values of the order. Convergent expansions are obtained for B-n(nz + 1/2) and E-n(nz + 1/2) in powers of n(-1), and coefficients are rational functions of z and...
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Bernoulli and Euler polynomials are considered for large values of the order. Convergent expansions are obtained for B-n(nz + 1/2) and E-n(nz + 1/2) in powers of n(-1), and coefficients are rational functions of z and hyperbolic functions of argument 1/(2z). These expansions are uniformly valid for \z +/- i/2 pi\ > 1/2 pi and \z +/- i/pi\ > 1/pi, respectively. For a real argument, the accuracy of these approximations is restricted to the monotonic region. The range of validity of the uniformity parameter z is enlarged, respectively, to regions of the form \z +/- i/2(m + 1)pi\ > 1/2(m + 1)pi and \z +/- i/(2m + 1)pi\ > 1/(2m + 1)pi, m = 1, 2, 3, ..., by adding certain combinations of incomplete gamma functions to these uniform expansions. In addition, the convergence of these improved expansions is stronger, and for a real argument, the accuracy of these improved approximations is also better in the oscillatory region.
In this paper, six new Redheffer-type inequalities involving circular functions and hyperbolic functions are established. (C) 2008 Elsevier Ltd. All rights reserved.
In this paper, six new Redheffer-type inequalities involving circular functions and hyperbolic functions are established. (C) 2008 Elsevier Ltd. All rights reserved.
Several inequalities involving hyperbolic functions are derived. Some of them are obtained with the aid of Stolarsky and Gini means. (C) 2012 Elsevier Inc. All rights reserved.
Several inequalities involving hyperbolic functions are derived. Some of them are obtained with the aid of Stolarsky and Gini means. (C) 2012 Elsevier Inc. All rights reserved.
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