Rational Approximations to the Exponential Function with Two Complex Conjugate Interpolation Points

1985 ◽  
Vol 16 (4) ◽  
pp. 814-821 ◽  
Author(s):  
Ernst Hairer ◽  
Arieh Iserles ◽  
Syvert P. Nørsett
Keyword(s):  
Exponential Function ◽  
Complex Conjugate ◽  
Rational Approximations

On theA 0-acceptability of rational approximations to the exponential function with only real poles

1988 ◽  
Vol 28 (1) ◽  
pp. 69-79 ◽  
Author(s):  
Laurence A. Bales ◽  
Ohannes A. Karakashian ◽  
Steven M. Serbin
Keyword(s):  
Exponential Function ◽  
Rational Approximations ◽  
Real Poles

scholarly journals Rational approximations of the exponential function at rational points

2017 ◽  
Vol 179 ◽  
pp. 220-239 ◽  
Author(s):  
Kalle Leppälä ◽  
Tapani Matala-aho ◽  
Topi Törmä
Keyword(s):  
Exponential Function ◽  
Rational Points ◽  
Rational Approximations

Simultaneous diophantine approximations and Hermite's method

1980 ◽  
Vol 21 (3) ◽  
pp. 463-470 ◽  
Author(s):  
Alain Durand
Keyword(s):  
Exponential Function ◽  
Integer Point ◽  
Rational Numbers ◽  
Rational Points ◽  
Rational Approximations ◽  
Diophantine Approximations ◽  
Simultaneous Diophantine Approximations ◽  
Image Position

In this paper we generalize a result of Mahler on rational approximations of the exponential function at rational points by proving the following theorem: let n ε N* and αl, …, αn be distinct non-zero rational numbers; there exists a constant c = c(n, αl, …, αn) ≥ 0 such thatfor every non-zero integer point (qo, ql, …, qn)and q = max {|ql|, … |qn|, 3}.

scholarly journals Note on rational approximations of the exponential function at rational points

1976 ◽  
Vol 14 (3) ◽  
pp. 449-455 ◽  
Author(s):  
Alain Durand
Keyword(s):  
Exponential Function ◽  
Rational Points ◽  
Rational Approximations ◽  
Image Position ◽  
Positive Integers

Let p, q, u, and v be any four positive integers, and let δ be a number in the interval 0 < δ ≤ 2. In one of his papers, Kurt Mahler, Bull. Austral. Math. Soc. 10 (1974), 325–335, proved that if q satisfies the inequalitiesthenIn this note, by a slightly different treatment of some inequalities in Mahler's paper, we easily obtain the same result with q only restricted by the first condition.

The Application of Continued Fractions to Wave Propagation in a Semi-Infinite Elastic Cylindrical Membrane

1969 ◽  
Vol 36 (3) ◽  
pp. 420-424 ◽  
Author(s):  
J. E. Akin ◽  
J. Counts
Keyword(s):  
Wave Propagation ◽  
Laplace Transform ◽  
Exponential Function ◽  
Continued Fractions ◽  
Wave Speed ◽  
Axial Stress ◽  
Rational Approximations ◽  
Stress Resultant ◽  
The Laplace Transform ◽  
Standard Techniques

The Laplace transform of the axial stress resultant in an impacting semi-infinite elastic cylindrical membrane is generated in the form of an exponential function involving the wave speed, and a series in powers of the reciprocal of the transform parameter. Continued fractions are used to obtain rational approximations for the transform represented by the series. The rational approximations, which are in the form of the ratio of two polynomials, are inverted by standard techniques. Results are presented for the axial stress resultant for small and large values of time and are compared with previously published results.

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