K. MAHLER, Zur Approximation der Exponentialfunktion und des Logarithmus I, II, J. Reine Angew. Math., 166 (1931), pp. 118--37, 138--50.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....most famous for the role they have played in Hermite s proof of the transcendence of the number e in [7] In Hermite s proof the polynomials q j;n j of type II have played the decisive role. A proof of the transcendence of e based on the polynomials p j;n j has later been given by K. Mahler [10]. Since these pioneering days the concept of Hermite Pad e approximants has kept a place in number theory (cf. for instance, 10, 11, 12] 4] 8] and in approximation theory (cf. the survey about publications in approximation theory in [2] and a survey about asymptotic results in [1] ....

....the polynomials q j;n j of type II have played the decisive role. A proof of the transcendence of e based on the polynomials p j;n j has later been given by K. Mahler [10] Since these pioneering days the concept of Hermite Pad e approximants has kept a place in number theory (cf. for instance, [10, 11, 12], 4] 8] and in approximation theory (cf. the survey about publications in approximation theory in [2] and a survey about asymptotic results in [1] Detailed studies of quadratic approximants and especially the polynomials pn ; q n ; r n have been done in [3] 5] 6] 19] and [17] In ....

Mahler, K., Zur Approximation der Exponentialfunktion und des Logarithmus I, II, J. Reine Angew. Math., 166 (1931), 118-37, 138-50.

....most famous for the role they have played in Hermite s proof of the transcendence of the number e in [8] In Hermite s proof the polynomials q j;n j of type II have played the decisive role. A proof of the transcendence of e based on the polynomials p j;n j of type I was given later by K. Mahler [11]. Since these pioneering days the concept of Hermite Pad e approximants has kept a place in number theory (cf. for instance, 11, 12, 13] 5] 9] and in approximation theory (cf. the survey about publications in approximation theory in [3] and a survey about asymptotic results in [1] ....

....polynomials q j;n j of type II have played the decisive role. A proof of the transcendence of e based on the polynomials p j;n j of type I was given later by K. Mahler [11] Since these pioneering days the concept of Hermite Pad e approximants has kept a place in number theory (cf. for instance, [11, 12, 13], 5] 9] and in approximation theory (cf. the survey about publications in approximation theory in [3] and a survey about asymptotic results in [1] Detailed studies of quadratic approximants and especially of the polynomials pn ; q n ; r n have been done in [4] 19] 6] and [7] In [4] ....

Mahler, K., Zur Approximation der Exponentialfunktion und des Logarithmus I, II, J. Reine Angew. Math., 166 (1931), 118-37, 138-50.

....2, is a Liouville number. 3 Michel Dekking has kindly pointed out a minor, easily repairable flaw in his proof. NUMBER THEORY AND FORMAL LANGUAGES 11 Becker conjectures (personal communication, 1993) that in fact these numbers, when transcendental, are S numbers in Mahler s classification ([72], 58, p. 63] Recently there have been some other interesting results on real numbers whose base b expansions are k automatic. Denoting the set of such numbers as L(k; b) we have the following theorem of Lehr [63] Theorem 6.1. The set L(k; b) forms a Q vector space. However, it can be shown ....

K. Mahler. Zur Approximation der Exponentialfunktion und des Logarithmus. I. J. Reine Angew. Math. 166 (1931/32), 118--136.

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K. MAHLER, Zur Approximation der Exponentialfunktion und des Logarithmus I, II, J. Reine Angew. Math., 166 (1931), pp. 118--37, 138--50.

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