Topic
Inverse hyperbolic function
About: Inverse hyperbolic function is a research topic. Over the lifetime, 833 publications have been published within this topic receiving 12737 citations.
Papers published on a yearly basis
1 / 2
Papers
18 May 1971
TL;DR: This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arCTanh, In, exp and square-root.
Abstract: This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arctanh, In, exp and square-root The basis for the algorithm is coordinate rotation in a linear, circular, or hyperbolic coordinate system depending on which function is to be calculated The only operations required are shifting, adding, subtracting and the recall of prestored constants The limited domain of convergence of the algorithm is calculated, leading to a discussion of the modifications required to extend the domain for floating point calculations
1,149 citations
TL;DR: In this paper, the authors provide derivations of elasticities in common applications of the inverse hyperbolic sine transformation and show empirically that the difference in elasticities driven by ad hoc transformations can be substantial.
Abstract: Applied econometricians frequently apply the inverse hyperbolic sine (or arcsinh) transformation to a variable because it approximates the natural logarithm of that variable and allows retaining zero‐valued observations. We provide derivations of elasticities in common applications of the inverse hyperbolic sine transformation and show empirically that the difference in elasticities driven by ad hoc transformations can be substantial. We conclude by offering practical guidance for applied researchers.
952 citations
894 citations
Book•
29 Nov 1974
TL;DR: Inverse Mellin Transform Analysis as discussed by the authors, the Gamma Function and Gamma Function are used to transform the Mellin transform into a generalized function, which is then used to obtain a generalized version of Bessel Function.
Abstract: I. Mellin Transforms.- Some Applications of the Mellin Transform Analysis.- 1.1 General Formulas.- 1.2 Algebraic Functions and Powers of Arbitrary Order.- 1.3 Exponential Functions.- 1.4 Logarithmic Functions.- 1.5 Trigonometric Functions.- 1.6 Hyperbolic Functions.- 1.7 The Gamma Function and Related Functions.- 1.8 Legendre Functions.- 1.9 Orthogonal Polynomials.- 1.10 Bessel Functions.- 1.11 Modified Bessel Function.- 1.12 Functions Related to Bessel Function.- 1.13 Whittaker Functions and Special Cases.- 1.14 Elliptic Integrals and Elliptic Functions.- 1.15 Hyper geometric Functions.- II. Inverse Mellin Transforms.- 2.1 General Formulas.- 2.2 Algebraic Functions and Powers of Arbitrary Order.- 2.3 Exponential and Logarithmic Functions.- 2.4 Trigonometric and Hyperbolic Functions.- 2.5 The Gamma Function and Related Functions.- 2.6 Orthogonal Polynomials and Legendre Functions.- 2.7 Bessel Functions and Related Functions.- 2.8 Whittaker Functions and Special Cases.
508 citations
Book•
1 Jan 1994
TL;DR: Cauchy Problem for Single First Order Equations Cauchy problem for Reducible Quasilinear Hyperbolic Systems as mentioned in this paper for general QH systems with Dissipation Mixed Initial-Boundary Value Problem with Boundary Dissipation for QuasILBolic Systems Typical Boundary value Problem and Typical Free Boundary Problem for RedUCible QuASILINear HSBs Generalized Riemann Problem for the System of One-Dimensional Isentropic Flow Typical free boundary problem for General QHSBs Bibliography Index.
Abstract: Cauchy Problem for Single First Order Equations Cauchy Problem for Reducible Quasilinear Hyperbolic Systems Cauchy Problem for General Quasilinear Hyperbolic Systems Cauchy Problem for Quasilinear Hyperbolic Systems with Dissipation Mixed Initial-Boundary Value Problem with Boundary Dissipation for Quasilinear Hyperbolic Systems Typical Boundary Value Problem and Typical Free Boundary Problem for Reducible Quasilinear Hyperbolic Systems Generalized Riemann Problem for the System of One-Dimensional Isentropic Flow Typical Free Boundary Problem and Generalized Riemann Problem for General Quasilinear Hyperbolic Systems Bibliography Index.
486 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 5 |
| 2024 | 5 |
| 2023 | 4 |
| 2022 | 19 |
| 2021 | 7 |
| 2020 | 9 |