Results 111 to 120 of about 196,126 (161)
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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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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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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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Exponentials and Bessel Functions
The Fibonacci Quarterly, 1976Davis, Bro. Basil, Hoggatt, V. E. jun.
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The American Mathematical Monthly, 1957
(1957). The Exponential Function. The American Mathematical Monthly: Vol. 64, No. 3, pp. 158-160.
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(1957). The Exponential Function. The American Mathematical Monthly: Vol. 64, No. 3, pp. 158-160.
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2014
By now we know Euler’s number \(\mathrm{e} =\mathrm{ e}^{1}\) quite well. In this chapter we define the exponential function \(\mathrm{e}^{x}\) for any x ∈ R, and its inverse the natural logarithmic function ln(x), for x > 0. (In the first section of the chapter we take a concise approach to the exponential function; in the second section we do things ...
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By now we know Euler’s number \(\mathrm{e} =\mathrm{ e}^{1}\) quite well. In this chapter we define the exponential function \(\mathrm{e}^{x}\) for any x ∈ R, and its inverse the natural logarithmic function ln(x), for x > 0. (In the first section of the chapter we take a concise approach to the exponential function; in the second section we do things ...
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ITERATION OF THE EXPONENTIAL FUNCTION
The Quarterly Journal of Mathematics, 1947openaire +1 more source