Results 131 to 140 of about 1,609 (176)

Approximation of Entire Functions of Exponential Type by Trigonometric Polynomials

Sampling Theory in Signal and Information Processing, 2007
Let f be an entire function of exponential type σ bounded on the real line. We associate with f an explicitly given function fL,0 which coincides with a trigonometric polynomial of period L and exponential type σ + 2π/L on the strip ℜz ≤ L/2 and which is zero outside.
Gerhard Schmeisser, Schmeisser Gerhard
exaly   +2 more sources

Operator Sine Functions and Exponential Trigonometric Pairs

Journal of Mathematical Sciences, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kostin, V. A., Kostin, A. V., Kostin, D. V.   +2 more
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The generalized exponential function and fractional trigonometric identities

2011 20th European Conference on Circuit Theory and Design (ECCTD), 2011
In this work, we recall the generalized exponential function in the fractional-order domain which enables defining generalized cosine and sine functions. We then re-visit some important trigonometric identities and generalize them from the narrow integer-order subset to the more general fractional-order domain. Generalized hyperbolic function relations
Ahmed G. Radwan, Ahmed S. Elwakil
openaire   +1 more source

On fractional derivatives of trigonometric functions and exponential functions

Chaos: An Interdisciplinary Journal of Nonlinear Science
In some places, fractional derivative is abbreviated as Dα, dαdtα(ordαdxα), where α is positive but not an integer. The “formulas” dαsin⁡tdtα=sin⁡(t+πα2), dαcos⁡tdtα=cos⁡(t+πα2), and dαeλtdtα=λαeλt are sometimes used. However, they generally hold for α∈Z+={0,1,2,…}.
Changpin Li, Jianhua Tang
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A NOTE ON TWO RESULTS ASSOCIATED WITH EXPONENTIAL AND TRIGONOMETRIC FUNCTIONS

Far East Journal of Mathematical Sciences (FJMS), 2016
Summary: The objective of this note is to show how we can establish Taylor-Maclaurin series expansions of products of exponential and trigonometric functions in an elementary way.
Sukanya, M., Choi, Junesang, Rathie, Arjun K.   +2 more
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On An Interpolation of a Function by Exponential-Trigonometric Natural Splines

UZBEK MATHEMATICAL JOURNAL
ne of the challenges in approximation is the interpolation problem. Splines are often used for function approximation. The theory of splines includes both algebraic and variational approaches. In both cases, the existence, uniqueness, and convergence of splines, along with algorithms for their construction, are studied based on their inherent ...
Shadimetov, Kholmat M., Boltaev, Aziz K.
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Basic Exponential and Trigonometric Functions

2003
In this chapter we shall introduce the basic exponential and basic trigonometric functions as solutions of a difference analog of the equation for harmonic motion on a q-quadratic grid. Some of their elementary properties will be derived in order to form the basis for developing the theory of basic Fourier series and study some of their applications in
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Generalized Exponential and Trigonometric Functions

1993
One of the most classical papers written on generalized Fibonacci numbers is that of A. F. Horadam, [8]. In that paper, one will find several of the following properties needed in order to obtain the results found in this article. We start with a special case of the basic definition found in [8].
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Real Exponential, Logarithmic, and Trigonometric Functions for Physicists

2022
Real Exponential, Logarithmic, and Trigonometric Functions for Physicists builds on the author's previous books focused on mathematics for scientists. This new work presents a rigorous study of the underlying mathematical functions used in physics and provides its readers a deeper understanding for those studying and practicing the physical sciences.
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Using Differentials to Differentiate Trigonometric and Exponential Functions

The College Mathematics Journal, 2013
Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential eq...
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