Showing papers on "Inverse trigonometric functions published in 1974"
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.
409 citations
Patent•
03 Jun 1974
TL;DR: In this article, a method and apparatus for obtaining the angle of attack of an aircraft developed as a result of an appropriate processing of the vertical speed, the airspeed, and the pitch attitude of the aircraft is described.
Abstract: This invention relates to a method and apparatus for obtaining the angle of attack of an aircraft developed as a result of an appropriate processing of the vertical speed, the airspeed, and the pitch attitude of the aircraft. The latter involves resolving the inverse sine of the vertical speed signal over the airspeed signal, and subsequently differentially combining the end product of the inverse sine computation and the chord line angle signal. The air speed signal is corrected by a corrective network which receives a feedback signal proportional to the angle of attack as well as a signal proportional to drift angle.
11 citations
TL;DR: In this paper, a unified treatment of many problems in digital pulse recording is presented, characterized by a reciprocal-space transfer function, which may be abstracted from published studies of sine wave recording.
Abstract: In this paper we present a unified treatment of many problems in digital pulse recording. The physics appropriate to each problem is characterized by a reciprocal-space transfer function, which may be abstracted from published studies of sine wave recording. Over twenty-five transfer functions are given in appendices. Given the transfer functions, an inverse Fourier transformation completes each problem. The fields, fluxes, and output voltage due to an arctangent magnetization profile in a tape of unit permeability are derived. A closely related case, that of a linear ramp magnetization, is treated briefly. A step function magnetization is considered for a tape of nonunit permeability in which, dependent upon the boundary conditions, demagnetization and remagnetization occur. Extensions of the theory of multitransition waveforms are undertaken, yielding the spectra of both regular and random sequences.
9 citations