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Subject Item
dbr:Doubly_periodic_function
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yago:Relation100031921 yago:MathematicalRelation113783581 yago:WikicatAnalyticFunctions yago:Function113783816 yago:Abstraction100002137
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双周期函数 Doubly periodic function Función doblemente periódica
rdfs:comment
In mathematics, a doubly periodic function is a function defined on the complex plane and having two "periods", which are complex numbers u and v that are linearly independent as vectors over the field of real numbers. That u and v are periods of a function ƒ means that for all values of the complex number z. En matemáticas, una función doblemente periódica es una aplicación definida en el plano complejo caracterizada por poseer dos "períodos",​ que son dos números complejos linealmente independientes si son considerados como vectores sobre el campo de los números reales. La existencia de estos dos períodos complejos de la función ƒ, denominados aquí u y v, significa que para todos los valores del número complejo z. 双周期函数是数学中对一类定义在复平面上的函数（复变量函数）的称呼，是在复平面的两个不同“方向”上都有周期性变化的函数。直观上可以理解为平面上“网格状”变化的函数。双周期函数是定义域为实数的周期函数在复变量函数中的推广。在复变量函数中，只有一个周期的函数称为单周期函数，如指数函数，周期是2πi。
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dbo:abstract
En matemáticas, una función doblemente periódica es una aplicación definida en el plano complejo caracterizada por poseer dos "períodos",​ que son dos números complejos linealmente independientes si son considerados como vectores sobre el campo de los números reales. La existencia de estos dos períodos complejos de la función ƒ, denominados aquí u y v, significa que para todos los valores del número complejo z. 双周期函数是数学中对一类定义在复平面上的函数（复变量函数）的称呼，是在复平面的两个不同“方向”上都有周期性变化的函数。直观上可以理解为平面上“网格状”变化的函数。双周期函数是定义域为实数的周期函数在复变量函数中的推广。在复变量函数中，只有一个周期的函数称为单周期函数，如指数函数，周期是2πi。 In mathematics, a doubly periodic function is a function defined on the complex plane and having two "periods", which are complex numbers u and v that are linearly independent as vectors over the field of real numbers. That u and v are periods of a function ƒ means that for all values of the complex number z. The doubly periodic function is thus a two-dimensional extension of the simpler singly periodic function, which repeats itself in a single dimension. Familiar examples of functions with a single period on the real number line include the trigonometric functions like cosine and sine, In the complex plane the exponential function ez is a singly periodic function, with period 2πi.
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