Results 241 to 250 of about 230,404 (281)

On exponential sums for coefficients of general L-functions

International Journal of Number Theory, 2021
We investigate the order of exponential sums involving the coefficients of general [Formula: see text]-functions satisfying a suitable functional equation and give some new estimates, including refining certain results in preceding works [X. Ren and Y.
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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
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A new implementation for the logarithmic/exponential function generator

Analog Integrated Circuits and Signal Processing, 2014
This paper presents two new approximations for the logarithmic and exponential functions. These approximations require only a square rooter function, a scalar function and a constant. Thus, the realization of these functions in current-mode is simple, straightforward and uses less number of transistors.
Muhammad Taher Abuelma'atti, Noman Ali Tassaduq   +1 more
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Exponentially generated wave functions

The Journal of Chemical Physics, 1985
We consider several generalizations of the exponential ansatz in a rather formal way, giving several new wave functions which we call exponentially generated (EG) wave functions. There are three distinct ways of the exponential-type generations of the wave functions, two of which are new.
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General gamma functions, exponentials, and hypergeometric functions

Russian Mathematical Surveys, 1998
The \(u\)-gamma functions and the \(u\)-exponentials of one and several complex variables are introduced and deformations of general hypergeometric functions are then studied by them. In the case of functions of one variable, the infinite product representations of the gamma functions \(\Gamma_u\) are obtained and their asymptotic behavior is ...
Gelfand, I. M., Graev, M. I., Retakh, V. S.   +2 more
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GENERATING FUNCTIONS OF EXPONENTIAL TYPE FOR ORTHOGONAL POLYNOMIALS

Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2004
Let \(\{ P_n : n\in N_0, \deg P_n=n\}\) be a sequence of monic orthogonal polynomials for a given probability measure on \((-\infty, \infty)\). A function \(\psi(x, t)\) is a generating function of the polynomials \(P_n\) if \[ \psi(t,x)=\sum_{n=0}^\infty a_n t^n P_n(x). \] The following result is proved.
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Generalized Padé approximations to the exponential function

BIT, 1992
When investigating the linear stability properties of an implicit Runge- Kutta method, the method is applied with stepsize \(h\) to the scalar test equation \(y' = qy\), \(Re(q) < 0\). It is well known that the linear stability properties of a Runge-Kutta method are determined solely by the stability properties of the associated rational approximation ...
Butcher, J. C., Chipman, F. H.
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THE DOMAIN OF CONVERGENCE OF SERIES OF GENERALIZED EXPONENTIAL FUNCTIONS

Mathematics of the USSR-Sbornik, 1985
Let f(z) be an entire function of exponential type and of completely regular growth, let \(\bar D\) be its conjugate diagram and let \(\{\lambda_ n\}_ 1^{\infty}\) be a sequence of complex numbers such that \(\lim_{n\to \infty}(\ln n/\lambda_ n)=0.\) The author proves several theorems on the convex properties of the domain of convergence of the series \
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Estimation of the generalized exponential renewal function

Journal of Statistical Computation and Simulation, 2013
When the shape parameter is a non-integer of the generalized exponential (GE) distribution, the analytical renewal function (RF) usually is not tractable. To overcome this, the approximation method has been used in this paper. In the proposed model, the n-fold convolution of the GE cumulative distribution function (CDF) is approximated by n-fold ...
Conghua Cheng, Jinyuan Chen, Haiqing Zhao   +2 more
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On the design and generation of the double exponential function

IEEE Transactions on Instrumentation and Measurement, 1996
For the double exponential function f(t)=K(e/sup -at/-e/sup -bt/), which is used for impulse testing of electrical components and systems, we derive an approximate relation between the ratio y/sub m/=T/sub m//T/sub max/, where T/sub max/ and T/sub m/ are, respectively, the times to reach the peak value F/sub max/ and the value F/sub max//m on the tail ...
S.C. Dutta Roy, D.K. Bhargava
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