Zeros of the deformed exponential function
نویسندگان
چکیده
منابع مشابه
On the Zeros of the Sections of the Exponential Function
The Eneström-Kakeya theorem (the absolute value of any zero of a0+a1x+· · ·+akx, ai ∈ R is at most max( a0 a1 , a1 a2 , . . . , ak−1 ak ) ) implies |νj| ≤ k . It was shown by Szegö [8] that the numbers νj k cluster around the simple closed curve Γ = {z : |ze1−z| = 1, |z| ≤ 1} as k → ∞ and conversely each point of the Szegö curve is a limit point of the normalized zeros. Moreover Szegö [8] and a...
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1. M. Marden, The geometry of the zeros of a polynomial in a complex variable, Math. Surveys No. 3, Amer. Math. Soc., Providence, R. I., f949. 2. A. Ostrowski, Recherches sur la méthode de Graeffe et les zéros des polynômes et des séries de Laurent, Acta Math. 72 (1940), 99-257. 3. Z. Rubinstein, Analytic methods in the study of zeros of polynomials, Pacific J. Math. 13 (1963), 237-249. 4. W. S...
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A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems. Though the deformed exponential families are defined by deformed exponential functions, these functions do not satisfy the law of exponents in general...
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We derive the large n asymptotics of zeros of sections of a generic exponential sum. We divide all the zeros of the nth section of the exponential sum into “genuine zeros,” which approach, as n → ∞, the zeros of the exponential sum, and “spurious zeros,” which go to infinity as n → ∞. We show that the spurious zeros, after scaling down by the factor of n, approach a “rosette,” a finite collecti...
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It is of frequent occurrence in problems of both pure and applied mathematics that certain values sought may be specified and must be determined as the roots of a tran-scendental equation. In particular, the equation may be of the class in which the unknown is involved only through the medium of exponential or trigonometric functions, with coefficients which are power functions or essentially s...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2018.05.006