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Perpendicular ion heating in turbulence and reconnection: magnetic moment breaking by coherent fluctuations. [PDF]
J Plasma PhysMallet A +4 more
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Exact soliton, lump, and breather solutions of the (3 + 1)-dimensional Jimbo-Miwa equation via the bilinear neural network method. [PDF]
Sci RepHussein HH, Mekawey H, Elsheikh A.
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A Characterization of the Exponential Function
Journal of the London Mathematical Society, 1986Let E be the class of all entire functions \(f(t)=\sum^{\infty}_{k=0}a_ kt^ k\) with \(a_ 0=1\), \(a_ k>0\) for \(k=1,2,3,...\), and \(\int^{\infty}_{0}t^ k(f(t))^{-1}dt=1/a_ k, k=0,1,2,... \). A conjecture of Renyi and Vincze is verified by proving the exponential function \(f(t)=e^ t\) is the only member of E.
Miles, Joseph, Williamson, Jack
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On the Exponential Inequalities and the Exponential Function
The Mathematical Gazette, 1907Theorem. If a he any positive quantity not equal to 1, and x, y, z be any three rational quantities in descending order of magnitude, then
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1983
Let z denote the identity map on C. For every non-negative integer n, we define a polynomial function E n by $$ {E_n} = \sum\limits_{{k = 0}}^n {\frac{1}{{k!}}{z^k}} $$ Given an arbitrary complex number c, let n be such that n + 1 ≧ 2|c|, and let q be an arbitrary positive integer.
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Let z denote the identity map on C. For every non-negative integer n, we define a polynomial function E n by $$ {E_n} = \sum\limits_{{k = 0}}^n {\frac{1}{{k!}}{z^k}} $$ Given an arbitrary complex number c, let n be such that n + 1 ≧ 2|c|, and let q be an arbitrary positive integer.
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1995
It is a general problem to determine the continued fractions for values of classical functions suitably normalized. We shall describe a solution of this problem in a very special case which will allow us in particular to get the continued fraction for e.
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It is a general problem to determine the continued fractions for values of classical functions suitably normalized. We shall describe a solution of this problem in a very special case which will allow us in particular to get the continued fraction for e.
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The American Mathematical Monthly, 1975
(1975). On the Exponential Function. The American Mathematical Monthly: Vol. 82, No. 8, pp. 842-844.
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(1975). On the Exponential Function. The American Mathematical Monthly: Vol. 82, No. 8, pp. 842-844.
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Exponentials and Bessel Functions
The Fibonacci Quarterly, 1976Davis, Bro. Basil, Hoggatt, V. E. jun.
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