The Experts below are selected from a list of 6324 Experts worldwide ranked by ideXlab platform
Nobushige Kurokawa - One of the best experts on this subject based on the ideXlab platform.
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QUANTUM DEFORMATIONS OF CATALAN’S CONSTANT, MAHLER’S MEASURE AND THE HÖLDER–SHINTANI DOUBLE Sine Function
Proceedings of the Edinburgh Mathematical Society, 2020Co-Authors: Nobushige KurokawaAbstract:AbstractWe study quantum deformations of Catalan’s constant, Mahler’s measure and the double Sine Function. We establish quantum deformations of basic relations between these three objects.
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Normalized double Sine Functions
Proceedings of the Japan Academy Series A Mathematical Sciences, 2020Co-Authors: Nobushige Kurokawa, Shinya KoyamaAbstract:We express normalized double Sine Functions of integer periods (N 1 ,N 2 ) via the standard double Sine Function of period (1,1). As an application we give an Euler product expression using the di-logarithm for the double zeta Function ζ(s, F p N 1 ) ⊗ ζ(s, F P N 2 ) for a prime number p and integers N 1 , N 2 .
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values of the double Sine Function
Journal of Number Theory, 2007Co-Authors: Shinya Koyama, Nobushige KurokawaAbstract:Abstract We calculate basic values of the double Sine Function. The algebraicity for some special values is proved. Its behavior in the fundamental domain is also studied. Especially we show that it has just two extremes: one relative maximum and one relative minimum. Asymptotic formulas for these extremal values are proved.
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Euler's integrals and multiple Sine Functions
Proceedings of the American Mathematical Society, 2005Co-Authors: Shinya Koyama, Nobushige KurokawaAbstract:We show that Euler's famous integrals whose integrands contain the logarithm of the Sine Function are expressed via multiple Sine Functions.
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multiple zeta Functions the double Sine Function and the signed double poisson summation formula
Compositio Mathematica, 2004Co-Authors: Shinya Koyama, Nobushige KurokawaAbstract:We construct multiple zeta Functions as absolute tensor products of usual zeta Functions. The Euler product expression is established for the most basic case $\zeta(s,\mathbf{F}_p)\otimes\zeta(s,\mathbf{F}_q)$ by using the signed double Poisson summation formula and the theory of the double Sine Function.
Edigles Guedes - One of the best experts on this subject based on the ideXlab platform.
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More Sine Function at Rational Argument, Product of Gamma Functions and Infinite Product Representations
viXra, 2018Co-Authors: Edigles GuedesAbstract:I derived an identity involving gamma Functions and Sine Function at rational argument; hence, the representation of infinite product arose.
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Sine Function at Rational Argument, Finite Product of Gamma Functions and Infinite Product Representation
viXra, 2018Co-Authors: Edigles GuedesAbstract:I corrected the Theorem 21 of previous paper, obtaining an identity for Sine Function at rational argument involving finite sum of the gamma Functions; hence, the representation of infinite product arose.
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New Integral Representation for Inverse Sine Function, the Rate of Catalan's Constant by Archimedes Constant and Other Functions
viXra, 2015Co-Authors: Edigles GuedesAbstract:In present article, we developed infinite series representations for inverse Sine Function and other Functions. Our main goal is to get the hypergeometric representation for Catalan constant and hyperbolic Sine Function; and new integral representation for inverse Sine Function.
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On the Inverse Sine Function, π and Babylonian Identity
Bulletin of Mathematical Sciences and Applications, 2014Co-Authors: Edigles Guedes, K. Raja Rama GandhiAbstract:We evaluate the constant π using the Babylonian identity and the inverse Sine Function.
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On the Complete Elliptic Integrals and Babylonian Identity V: The Complete Elliptic Integral of first kind and Approximation by Inverse Sine Function
Bulletin of Mathematical Sciences and Applications, 2013Co-Authors: Edigles Guedes, K. Raja Rama GandhiAbstract:I approximate the complete elliptic integral of first kind using inverse Sine Function.
Shinya Koyama - One of the best experts on this subject based on the ideXlab platform.
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Normalized double Sine Functions
Proceedings of the Japan Academy Series A Mathematical Sciences, 2020Co-Authors: Nobushige Kurokawa, Shinya KoyamaAbstract:We express normalized double Sine Functions of integer periods (N 1 ,N 2 ) via the standard double Sine Function of period (1,1). As an application we give an Euler product expression using the di-logarithm for the double zeta Function ζ(s, F p N 1 ) ⊗ ζ(s, F P N 2 ) for a prime number p and integers N 1 , N 2 .
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values of the double Sine Function
Journal of Number Theory, 2007Co-Authors: Shinya Koyama, Nobushige KurokawaAbstract:Abstract We calculate basic values of the double Sine Function. The algebraicity for some special values is proved. Its behavior in the fundamental domain is also studied. Especially we show that it has just two extremes: one relative maximum and one relative minimum. Asymptotic formulas for these extremal values are proved.
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Euler's integrals and multiple Sine Functions
Proceedings of the American Mathematical Society, 2005Co-Authors: Shinya Koyama, Nobushige KurokawaAbstract:We show that Euler's famous integrals whose integrands contain the logarithm of the Sine Function are expressed via multiple Sine Functions.
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multiple zeta Functions the double Sine Function and the signed double poisson summation formula
Compositio Mathematica, 2004Co-Authors: Shinya Koyama, Nobushige KurokawaAbstract:We construct multiple zeta Functions as absolute tensor products of usual zeta Functions. The Euler product expression is established for the most basic case $\zeta(s,\mathbf{F}_p)\otimes\zeta(s,\mathbf{F}_q)$ by using the signed double Poisson summation formula and the theory of the double Sine Function.
Feng Qi - One of the best experts on this subject based on the ideXlab platform.
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monotonicity results and inequalities for the inverse hyperbolic Sine Function
Journal of Inequalities and Applications, 2013Co-Authors: Feng QiAbstract:In the paper, the authors present monotonicity results of a Function involving the inverse hyperbolic Sine. From these, the authors derive some inequalities for bounding the inverse hyperbolic Sine.
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full length article convexity of the generalized Sine Function and the generalized hyperbolic Sine Function
Journal of Approximation Theory, 2013Co-Authors: Weidong Jiang, Miaokun Wang, Yueping Jiang, Feng QiAbstract:In the paper, the authors prove that the generalized Sine Function sin"p","qx and the generalized hyperbolic Sine Function sinh"p","qx are respectively geometrically concave and geometrically convex. Consequently, the authors verify a conjecture posed by B. A. Bhayo and M. Vuorinen.
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sharpening and generalizations of shafer s inequality for the arc Sine Function
Integral Transforms and Special Functions, 2012Co-Authors: Feng QiAbstract:In this paper, by a concise and elementary approach, we sharpen and generalize Shafer's inequality for the arc Sine Function, and some known results are extended and generalized.
Peter M Nilsson - One of the best experts on this subject based on the ideXlab platform.
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parabolic synthesis methodology implemented on the Sine Function
International Symposium on Circuits and Systems, 2009Co-Authors: Erik Hertz, Peter M NilssonAbstract:This paper introduces a parabolic synthesis methodology for implementation of approximations of unary Functions like trigonometric Functions and logarithms, which are specialized for efficient hardware mapped VLSI design. The advantages with the methodology are, short critical path, fast computation and high throughput enabled by a high degree of architectural parallelism. The feasibility of the methodology is shown by developing an approximation of the Sine Function for implementation in hardware.
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ISCAS - Parabolic synthesis methodology implemented on the Sine Function
2009 IEEE International Symposium on Circuits and Systems, 2009Co-Authors: Erik Hertz, Peter M NilssonAbstract:This paper introduces a parabolic synthesis methodology for implementation of approximations of unary Functions like trigonometric Functions and logarithms, which are specialized for efficient hardware mapped VLSI design. The advantages with the methodology are, short critical path, fast computation and high throughput enabled by a high degree of architectural parallelism. The feasibility of the methodology is shown by developing an approximation of the Sine Function for implementation in hardware.
