منابع مشابه
An Elliptic Function – The Weierstrass Function
Definition W.1 An elliptic function f (z) is a non constant meromorphic function on C that is doubly periodic. That is, there are two nonzero complex numbers ω 1 , ω 2 whose ratio is not real, such that f (z + ω 1) = f (z) and f (z + ω 2) = f (z). Fix two real numbers β, γ > 0. The Weierstrass function with primitive periods γ and iβ is the function ℘ : C → C defined by ℘(z) = 1 z 2 + ω∈γZ Z⊕iβ...
متن کاملParametrized Dynamics of the Weierstrass Elliptic Function
We study parametrized dynamics of the Weierstrass elliptic ℘ function by looking at the underlying lattices; that is, we study parametrized families ℘Λ and let Λ vary. Each lattice shape is represented by a point τ in a fundamental period in modular space; for a fixed lattice shape Λ = [1, τ ] we study the parametrized space kΛ. We show that within each shape space there is a wide variety of dy...
متن کاملThe zeros of the Weierstrass ℘–function and hypergeometric series
We express the zeros of the Weierstass ℘-function in terms of generalized hypergeometric functions. As an application of our main result we prove the transcendence of two specific hypergeometric functions at algebraic arguments in the unit disc. We also give a Saalschützian 4F3–evaluation.
متن کاملWeierstrass Semigroups in an Asymptotically Good Tower of Function Fields
The Weierstrass semigroups of some places in an asymptotically good tower of function fields are computed. 0. Introduction A tower F1 ⊆ F2 ⊆ F3 ⊆ . . . of algebraic function fields over a finite field Fl is said to be asymptotically good if lim m→∞ number of rational places of Fm/Fl genus of Fm > 0. Recently an explicit description was obtained of several asymptotically good towers {1}, {2}. Th...
متن کاملGenerating signals with multiscale time irreversibility: The asymmetric weierstrass function
Time irreversibility (asymmetry with respect to time reversal) is an important property of many time series derived from processes in nature. Some time series (e.g., healthy heart rate dynamics) demonstrate even more complex, multiscale irreversibility, such that not only the original but also coarse-grained time series are asymmetric over a wide range of scales. Several indices to quantify mul...
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ژورنال
عنوان ژورنال: Applications of Mathematics
سال: 1971
ISSN: 0862-7940,1572-9109
DOI: 10.21136/am.1971.103355